Atomtronics deals with matter-wave circuits of ultracold atoms manipulated through magnetic or laser-generated guides with different shapes and intensities. In this way, new types of quantum networks can be constructed in which coherent fluids are controlled with the know-how developed in the atomic and molecular physics community. In particular, quantum devices with enhanced precision, control, and flexibility of their operating conditions can be accessed. Concomitantly, new quantum simulators and emulators harnessing on the coherent current flows can also be developed. Here, the authors survey the landscape of atomtronics-enabled quantum technology and draw a roadmap for the field in the near future. The authors review some of the latest progress achieved in matter-wave circuits{\textquoteright} design and atom-chips. Atomtronic networks are deployed as promising platforms for probing many-body physics with a new angle and a new twist. The latter can be done at the level of both equilibrium and nonequilibrium situations. Numerous relevant problems in mesoscopic physics, such as persistent currents and quantum transport in circuits of fermionic or bosonic atoms, are studied through a new lens. The authors summarize some of the atomtronics quantum devices and sensors. Finally, the authors discuss alkali-earth and Rydberg atoms as potential platforms for the realization of atomtronic circuits with special features.

}, doi = {10.1116/5.0026178}, url = {https://doi.org/10.1116/5.0026178}, author = {L. Amico and M. Boshier and G. Birkl and A. Minguzzi and C. Miniatura and L.-C. Kwek and D. Aghamalyan and V. Ahufinger and D. Anderson and N. Andrei and A. S. Arnold and M. Baker and T. A. Bell and T. Bland and J. P. Brantut and D. Cassettari and W. J. Chetcuti and F. Chevy and R. Citro and S. De Palo and R. Dumke and M. Edwards and R. Folman and J. Fortagh and S. A. Gardiner and B. M. Garraway and G. Gauthier and A. G{\"u}nther and T. Haug and C. Hufnagel and M. Keil and P. Ireland and M. Lebrat and W. Li and L. Longchambon and J. Mompart and O. Morsch and P. Naldesi and T. W. Neely and M. Olshanii and E. Orignac and S. Pandey and A. P{\'e}rez-Obiol and H. Perrin and L. Piroli and J. Polo and A. L. Pritchard and N. P. Proukakis and C. Rylands and H. Rubinsztein-Dunlop and F. Scazza and S. Stringari and F. Tosto and A. Trombettoni and N. Victorin and W. von Klitzing and D. Wilkowski and K. Xhani and A. Yakimenko} } @article {339, title = {Artificial gauge field switching using orbital angular momentum modes in optical waveguides}, journal = {Light: Science \& Applications}, volume = {9}, year = {2020}, month = {2020/08/28}, pages = {150}, abstract = {The discovery of artificial gauge fields controlling the dynamics of uncharged particles that otherwise elude the influence of standard electromagnetic fields has revolutionised the field of quantum simulation. Hence, developing new techniques to induce these fields is essential to boost quantum simulation of photonic structures. Here, we experimentally demonstrate the generation of an artificial gauge field in a photonic lattice by modifying the topological charge of a light beam, overcoming the need to modify the geometry along the evolution or impose external fields. In particular, we show that an effective magnetic flux naturally appears when a light beam carrying orbital angular momentum is injected into a waveguide lattice with a diamond chain configuration. To demonstrate the existence of this flux, we measure an effect that derives solely from the presence of a magnetic flux, the Aharonov-Bohm caging effect, which is a localisation phenomenon of wavepackets due to destructive interference. Therefore, we prove the possibility of switching on and off artificial gauge fields just by changing the topological charge of the input state, paving the way to accessing different topological regimes in a single structure, which represents an important step forward for optical quantum simulation.

}, isbn = {2047-7538}, doi = {https://doi.org/10.1038/s41377-020-00385-6}, url = {https://www.nature.com/articles/s41377-020-00385-6}, author = {C. J{\"o}rg and G. Queralt{\'o} and M. Kremer and G. Pelegr{\'\i} and J. Schulz and A. Szameit and G. von Freymann and J. Mompart and V. Ahufinger} } @article {338, title = {Effective triangular ladders with staggered flux from spin-orbit coupling in 1D optical lattices}, journal = {The European Physical Journal D}, volume = {74}, year = {2020}, chapter = {123}, abstract = {Light-induced spin-orbit coupling is a flexible tool to study quantum magnetism with ultracold atoms. In this work we show that spin-orbit coupled Bose gases in a one-dimensional optical lattice can be mapped into a two-leg triangular ladder with staggered flux following a lowest-band truncation of the Hamiltonian. The effective flux and the ratio of the tunneling strengths can be independently adjusted to a wide range of values. We identify a certain regime of parameters where a hard-core boson approximation holds and the system realizes a frustrated triangular spin ladder with tunable flux. We study the properties of the effective spin Hamiltonian using the density-matrix renormalization-group method and determine the phase diagram at half-filling. It displays two phases: a uniform superfluid and a bond-ordered insulator. The latter can be stabilized only for low Raman detuning. Finally, we provide experimentally feasible trajectories across the parameter space of the SOC system that cross the predicted phase transition.

}, doi = {10.1140/epjd/e2020-10129-1}, url = {https://link.springer.com/article/10.1140/epjd/e2020-10129-1}, author = {J. Cabedo and J. Claramunt and J. Mompart and V. Ahufinger and A. Celi} } @article {337, title = {Orbital angular momentum dynamics of Bose-Einstein condensates trapped in two stacked rings}, journal = {Physical Review A}, volume = {102}, year = {2020}, chapter = {023331 }, abstract = {We investigate the stability and dynamics of the orbital angular momentum modes of a repulsive Bose-Einstein condensate trapped in two tunnel-coupled rings in a stack configuration. Within mean-field theory, we derive a two-state model for the system in the case in which we populate both rings equally with a single orbital angular momentum mode and include small perturbations in other modes. Analyzing the fixed-point solutions of the model and the associated classical Hamiltonian, we characterize the destabilization of the stationary states and the subsequent dynamics. By populating a single orbital angular momentum mode with an arbitrary population imbalance between the rings, we derive analytically the boundary between the regimes of Josephson oscillations and macroscopic quantum self-trapping and study numerically the stability of these solutions.

}, doi = {10.1103/PhysRevA.102.023331}, url = {https://link.aps.org/doi/10.1103/PhysRevA.102.023331}, author = {N. Eul{\`a}lia and J. Mompart and B. Juli{\'a}-D{\'\i}az and V. Ahufinger} } @article {333, title = {Topological state engineering via supersymmetric transformations}, journal = {Communication Physics}, volume = {3}, year = {2020}, chapter = {49}, abstract = {The quest to explore new techniques for the manipulation of topological states simultaneously promotes a deeper understanding of topological physics and is essential in identifying new ways to harness their unique features. Here, we examine the potential of supersymmetric transformations to systematically address, alter and reconfigure the topological properties of a system. To this end, we theoretically and experimentally study the changes that topologically protected states in photonic lattices undergo as supersymmetric\ transformations are applied to their host system. In particular, we show how supersymmetry-induced phase transitions can selectively suspend and re-establish the\ topological protection of specific states. Furthermore, we reveal how understanding the interplay between internal symmetries and the symmetry constraints of supersymmetric transformations provides a roadmap to directly access the desirable topological properties of a system. Our findings pave the way for establishing supersymmetry-inspired techniques as a powerful and versatile tool for topological state engineering.

}, doi = {https://doi.org/10.1038/s42005-020-0316-4}, url = {https://www.nature.com/articles/s42005-020-0316-4$\#$citeas}, author = {G. Queralt{\'o} and M. Kremer and L. J. Maczewsky and M. Heinrich and J. Mompart and V. Ahufinger and A. Szameit} } @article {322, title = {Coherent spin mixing via spin-orbit coupling in Bose gases}, journal = {Phys. Rev. A}, volume = {100}, year = {2019}, month = {Dec}, pages = {063633}, abstract = {We study beyond-mean-field properties of interacting spin-1 Bose gases with synthetic Rashba-Dresselhaus spin-orbit coupling at low energies. We derive a many-body Hamiltonian following a tight-binding approximation in quasimomentum space, where the effective spin dependence of the collisions that emerge from spin-orbit coupling leads to dominant correlated tunneling processes that couple the different bound states. We discuss the properties of the spectrum of the derived Hamiltonian and its experimental signatures. In a certain region of the parameter space, the system becomes integrable, and its dynamics becomes analogous to that of a spin-1 condensate with spin-dependent collisions. Remarkably, we find that such dynamics can be observed in existing experimental setups through quench experiments that are robust against magnetic fluctuations.

}, doi = {10.1103/PhysRevA.100.063633}, url = {https://link.aps.org/doi/10.1103/PhysRevA.100.063633}, author = {J. Cabedo and J. Claramunt and A. Celi and Y. Zhang and V. Ahufinger and J. Mompart} } @article {307, title = {Quantum magnetism with ultracold bosons carrying orbital angular momentum}, journal = {Phys. Rev. A}, volume = {100}, year = {2019}, month = {Aug}, pages = {023615}, doi = {10.1103/PhysRevA.100.023615}, url = {https://link.aps.org/doi/10.1103/PhysRevA.100.023615}, author = {G. Pelegr{\'\i} and J. Mompart and V. Ahufinger and A. J. Daley} } @article {323, title = {Second-order topological corner states with ultracold atoms carrying orbital angular momentum in optical lattices}, journal = {Phys. Rev. B}, volume = {100}, year = {2019}, month = {Nov}, pages = {205109}, abstract = {We propose a realization of a two-dimensional higher-order topological insulator with ultracold atoms loaded into orbital angular momentum (OAM) states of an optical lattice. The symmetries of the OAM states induce relative phases in the tunneling amplitudes that allow to describe the system in terms of two decoupled lattice models. Each of these models displays one-dimensional edge states and zero-dimensional corner states that are correlated with the topological properties of the bulk. We show that the topologically nontrivial regime can be explored in a wide range of experimentally feasible values of the parameters of the physical system. Furthermore, we propose an alternative way to characterize the second-order topological corner states based on the computation of the Zak{\textquoteright}s phases of the bands of first-order edge states.

}, doi = {10.1103/PhysRevB.100.205109}, url = {https://link.aps.org/doi/10.1103/PhysRevB.100.205109}, author = {G. Pelegr{\'\i} and A. M. Marques and V. Ahufinger and J. Mompart and R. G. Dias} } @article {302, title = {Topological edge states and Aharanov-Bohm caging with ultracold atoms carrying orbital angular momentum}, journal = {Phys. Rev. A}, volume = {99}, year = {2019}, month = {Feb}, pages = {023613}, abstract = {We show that bosonic atoms loaded into orbital angular momentum\ l=1\ states of a lattice in a diamond-chain geometry provide a flexible and simple platform for exploring a range of topological effects. This system exhibits robust edge states that persist across the gap-closing points, indicating the absence of a topological transition. We discuss how to perform the topological characterization of the model with a generalization of the Zak{\textquoteright}s phase and we show that this system constitutes a realization of a square-root topological insulator. Furthermore, the relative phases arising naturally in the tunneling amplitudes lead to the appearance of Aharanov-Bohm caging in the lattice. We discuss how these properties can be realized and observed in ongoing experiments.

}, doi = {10.1103/PhysRevA.99.023613}, url = {https://link.aps.org/doi/10.1103/PhysRevA.99.023613}, author = {G. Pelegr{\'\i} and A. M. Marques and R. G. Dias and A. J. Daley and J. Mompart and V. Ahufinger} } @article {301, title = {Topological edge states with ultracold atoms carrying orbital angular momentum in a diamond chain}, journal = {Phys. Rev. A}, volume = {99}, year = {2019}, month = {Feb}, pages = {023612}, abstract = {We study the single-particle properties of a system formed by ultracold atoms loaded into the manifold of\ l=1\ orbital angular momentum (OAM) states of an optical lattice with a diamond-chain geometry. Through a series of successive basis rotations, we show that the OAM degree of freedom induces phases in some tunneling amplitudes of the tight-binding model that are equivalent to a net\ π\ flux through the plaquettes. These effects give rise to a topologically nontrivial band structure and protected edge states which persist everywhere in the parameter space of the model, indicating the absence of a topological transition. By taking advantage of these analytical mappings, we also show that this system constitutes a realization of a square-root topological insulator. In addition, we demonstrate that quantum interferences between the different tunneling processes involved in the dynamics may lead to Aharanov-Bohm caging in the system. All these analytical results are confirmed by exact diagonalization numerical calculations.

}, doi = {10.1103/PhysRevA.99.023612}, url = {https://link.aps.org/doi/10.1103/PhysRevA.99.023612}, author = {G. Pelegr{\'\i} and A. M. Marques and R. G. Dias and A. J. Daley and V. Ahufinger and J. Mompart} } @article {280, title = {Atomic-frequency-comb quantum memory via piecewise adiabatic passage}, journal = {Phys. Rev. A}, volume = {98}, year = {2018}, month = {Oct}, pages = {043834}, abstract = {In this paper, we propose a method to create an atomic frequency comb (AFC) in hot atomic vapors using the piecewise adiabatic passage (PAP) technique. Due to the Doppler effect, the trains of pulses used for PAP give rise to a velocity-dependent transfer of the atomic population from the initial state to the target one, thus forming a velocity comb whose periodicity depends not only on the repetition rate of the applied pulses but also on the specific atomic transitions considered. We highlight the advantages of using this transfer technique with respect to standard methods and discuss, in particular, its application to store a single telecom photon in an AFC quantum memory using a high density Ba atomic vapor.

}, doi = {10.1103/PhysRevA.98.043834}, url = {https://link.aps.org/doi/10.1103/PhysRevA.98.043834}, author = {J. L. Rubio and D. Viscor and J. Mompart and V. Ahufinger} } @article {286, title = {Damping of Josephson Oscillations in Strongly Correlated One-Dimensional Atomic Gases}, journal = {Phys. Rev. Lett.}, volume = {121}, year = {2018}, month = {Aug}, pages = {090404}, abstract = {We study Josephson oscillations of two strongly correlated one-dimensional bosonic clouds separated by a localized barrier. Using a quantum-Langevin approach and the exact Tonks-Girardeau solution in the impenetrable-boson limit, we determine the dynamical evolution of the particle-number imbalance, displaying an effective damping of the Josephson oscillations which depends on barrier height, interaction strength, and temperature. We show that the damping originates from the quantum and thermal fluctuations intrinsically present in the strongly correlated gas. Because of the density-phase duality of the model, the same results apply to particle-current oscillations in a one-dimensional ring where a weak barrier couples different angular momentum states.

}, doi = {10.1103/PhysRevLett.121.090404}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.121.090404}, author = {J. Polo and V. Ahufinger and F. W. J. Hekking and A. Minguzzi} } @article {278, title = {Integrated photonic devices based on adiabatic transitions between supersymmetric structures}, journal = {Opt. Express}, volume = {26}, number = {26}, year = {2018}, month = {Dec}, pages = {33797{\textendash}33806}, abstract = {We introduce adiabatic transitions connecting two supersymmetric partner profiles by smoothly modifying the transverse refractive index profile along the propagation direction. With this transformation, one of the transverse electric modes evolves adapting its shape and propagation constant without being coupled to other guided or radiated modes while the rest of the modes are radiated. This technique offers a systematic way to manipulate the modal content in systems of optical waveguides and engineer efficient and robust photonic devices such as tapered waveguides, single-waveguide mode filters, beam splitters and interferometers. Numerical simulations show that very high fidelities and transmitted powers are obtained for a broad range of devices lengths and light{\textquoteright}s\ wavelengths.

}, keywords = {Femtosecond laser writing, Guided wave optics, Optical devices, Optical systems, Refractive index, Waveguide modes}, doi = {10.1364/OE.26.033797}, url = {http://www.opticsexpress.org/abstract.cfm?URI=oe-26-26-33797}, author = {G. Queralt{\'o} and V. Ahufinger and J. Mompart} } @article {279, title = {Quantum sensing using imbalanced counter-rotating Bose-Einstein condensate modes}, journal = {New Journal of Physics}, volume = {20}, number = {10}, year = {2018}, pages = {103001}, abstract = {A quantum device for measuring two-body interactions, scalar magnetic fields and rotations is proposed using a Bose-Einstein condensate (BEC) in a ring trap. We consider an imbalanced superposition of orbital angular momentum modes with opposite winding numbers for which a rotating minimal atomic density line appears. We derive an analytical model relating the angular frequency of the minimal density line rotation to the strength of the nonlinear atom-atom interactions and the difference between the populations of the counter-propagating modes. Additionally, we propose a full experimental protocol based on direct fluorescence imaging of the BEC that allows to measure all the quantities involved in the analytical model and use the system for sensing purposes.

}, url = {http://stacks.iop.org/1367-2630/20/i=10/a=103001}, author = {G. Pelegr{\'\i} and J. Mompart and V. Ahufinger} } @article {277, title = {Engineering of orbital angular momentum supermodes in coupled optical waveguides}, journal = {Scientific Reports}, volume = {7}, year = {2017}, month = {APR 26}, pages = {44057}, type = {Article}, abstract = {In this work we demonstrate the existence of orbital angular momentum (OAM) bright and dark supermodes in a three-evanescently coupled cylindrical waveguides system. Bright and dark supermodes are characterized by their coupling and decoupling from one of the waveguides, respectively. In addition, we demonstrate that complex couplings between modes of different waveguides appear naturally due to the characteristic spiral phase-front of OAM modes in two-dimensional configurations where the waveguides are arranged forming a triangle. Finally, by adding dissipation to the waveguide uncoupled to the dark supermode, we are able to filter this supermode out, allowing for the design of OAM mode cloners and inverters.

}, issn = {2045-2322}, doi = {10.1038/srep44057}, author = {A. Turpin and G. Pelegr{\'\i} and J. Polo and J. Mompart and V. Ahufinger} } @article {276, title = {Mode-division (de)multiplexing using adiabatic passage and supersymmetric waveguides}, journal = {Optics Express}, volume = {25}, number = {22}, year = {2017}, month = {OCT 30}, pages = {27396-27404}, type = {Article}, chapter = {27396}, abstract = {The development of mode-division multiplexing techniques is an important step to increase the information processing capacity. In this context, we design an efficient and robust mode-division (de) multiplexing integrated device based on the combination of spatial adiabatic passage and supersymmetric techniques. It consists of two identical step-index external waveguides coupled to a supersymmetric central one with a specific modal content that prevents the transfer of the fundamental transverse electric spatial mode. The separation between waveguides is engineered along the propagation direction to optimize spatial adiabatic passage for the first excited transverse electric spatial mode of the step-index waveguides. Thus, by injecting a superposition of the two lowest spatial modes into the step-index left waveguide, the fundamental mode remains in the left waveguide while the first excited mode is fully transmitted to the right waveguide. Output fidelities F \> 0.90 are obtained for a broad range of geometrical parameter values and light{\textquoteright}s wavelengths, reaching F = 0.99 for optimized values. (C) 2017 Optical Society of America

}, issn = {{1094-4087}}, doi = {10.1364/OE.25.027396}, author = {G. Queralt{\'o} and V. Ahufinger and J. Mompart} } @article {264, title = {Quantum optics and frontiers of physics: the third quantum revolution}, journal = {Physica Scripta}, volume = {92}, number = {1}, year = {2017}, pages = {013003}, abstract = {The year 2015 was the International Year of Light. However, it also marked, the 20th anniversary of the first observation of Bose{\textendash}Einstein condensation in atomic vapors by Eric Cornell, Carl Wieman and Wolfgang Ketterle. This discovery could be considered as one of the greatest achievements of quantum optics that has triggered an avalanche of further seminal discoveries and achievements. For this reason we devote this essay for the focus issue on {\textquoteleft}Quantum Optics in the International Year of Light{\textquoteright} to the recent revolutionary developments in quantum optics at the frontiers of all physics: atomic physics, molecular physics, condensed matter physics, high energy physics and quantum information science. We follow here the lines of the introduction to our book {\textquoteleft}Ultracold atoms in optical lattices: Simulating quantum many-body systems{\textquoteright} (Lewenstein et al 2012 Ultracold Atoms in Optical Lattices: Simulating Quantum Many-body Systems (Oxford: University Press)), and to a lesser extent the review article M Lewenstein et al (2007 Adv. Phys. 56 [http://https://dx.doi.org/10.1080/00018730701223200] 243 ). The book, however, was published in 2012, and many things has happened since then{\textemdash}the present essay is therefore upgraded to include the latest developments.

}, url = {http://stacks.iop.org/1402-4896/92/i=1/a=013003}, author = {A. Celi and A. Sanpera and V. Ahufinger and M. Lewenstein} } @article {250, title = {Single-atom edgelike states via quantum interference}, journal = {Phys. Rev. A}, volume = {95}, year = {2017}, month = {Jan}, pages = {013614}, abstract = {We demonstrate how quantum interference may lead to the appearance of robust edgelike states of a single ultracold atom in a two-dimensional optical ribbon. We show that these states can be engineered within the manifold of either local ground states of the sites forming the ribbon or states carrying one unit of angular momentum. In the former case, we show that the implementation of edgelike states can be extended to other geometries, such as tilted square lattices. In the latter case, we suggest using the winding number associated to the angular momentum as a synthetic dimension.

}, doi = {10.1103/PhysRevA.95.013614}, url = {http://link.aps.org/doi/10.1103/PhysRevA.95.013614}, author = {G. Pelegr{\'\i} and J. Polo and A. Turpin and M. Lewenstein and J. Mompart and V. Ahufinger} } @article {PhysRevA.93.033613, title = {Geometrically induced complex tunnelings for ultracold atoms carrying orbital angular momentum}, journal = {Phys. Rev. A}, volume = {93}, year = {2016}, month = {Mar}, pages = {033613}, publisher = {American Physical Society}, abstract = {We investigate the dynamics of angular momentum states for a single ultracold atom trapped in two-dimensional systems of sided coupled ring potentials. The symmetries of the system show that tunneling amplitudes between different ring states with variation of the winding number are complex. In particular, we demonstrate that in a triangular ring configuration the complex nature of the cross-couplings can be used to geometrically engineer spatial dark states to manipulate the transport of orbital angular momentum states via quantum interference.}, doi = {10.1103/PhysRevA.93.033613}, url = {http://link.aps.org/doi/10.1103/PhysRevA.93.033613}, author = {J. Polo and J. Mompart and V. Ahufinger} } @article {248, title = {Optimal conditions for spatial adiabatic passage of a Bose-Einstein condensate}, journal = {Phys. Rev. A}, volume = {94}, number = {5}, year = {2016}, month = {NOV 8}, type = {Article}, abstract = {We investigate spatial adiabatic passage of a Bose-Einstein condensate in a triple-well potential within the three-mode approximation. By rewriting the dynamics in the so-called time-dependent dark-dressed basis, we analytically derive the optimal conditions for the nonlinear parameter and the on-site energies of each well to achieve a highly efficient condensate transport. We show that the nonlinearity yields a high-efficiency plateau for the condensate transport as a function of the on-site energy difference between the outermost wells, favoring the robustness of the transport. We also analyze the case of different nonlinearities in each well, which, for certain parameter values, leads to an increase of the width of this plateau.

}, issn = {2469-9926}, doi = {10.1103/PhysRevA.94.053606}, author = {J. L. Rubio and V. Ahufinger and T. Busch and J. Mompart} } @article {244, title = {Spatial adiabatic passage: a review of recent progress}, journal = {Reports on Progress in Physics}, volume = {79}, year = {2016}, chapter = {074401}, abstract = {Adiabatic techniques are known to allow for engineering quantum states with high fidelity. This requirement is currently of large interest, as applications in quantum information require the preparation and manipulation of quantum states with minimal errors. Here we review recent progress on developing techniques for the preparation of spatial states through adiabatic passage, particularly focusing on three state systems. These techniques can be applied to matter waves in external potentials, such as cold atoms or electrons, and to classical waves in waveguides, such as light or sound

}, url = {http://stacks.iop.org/0034-4885/79/i=7/a=074401}, author = {R. Menchon-Enrich and A. Benseny and V. Ahufinger and A. D. Greentree and T. Busch and J. Mompart} } @article {1367-2630-18-1-015010, title = {Transport of ultracold atoms between concentric traps via spatial adiabatic passage}, journal = {New Journal of Physics}, volume = {18}, number = {1}, year = {2016}, pages = {015010}, abstract = {Spatial adiabatic passage processes for ultracold atoms trapped in tunnel-coupled cylindrically symmetric concentric potentials are investigated. Specifically, we discuss the matter-wave analog of the rapid adiabatic passage (RAP) technique for a high fidelity and robust loading of a single atom into a harmonic ring potential from a harmonic trap, and for its transport between two concentric rings. We also consider a system of three concentric rings and investigate the transport of a single atom between the innermost and the outermost rings making use of the matter-wave analog of the stimulated Raman adiabatic passage (STIRAP) technique. We describe the RAP-like and STIRAP-like dynamics by means of a two- and a three-state model, respectively, obtaining good agreement with the numerical simulations of the corresponding two-dimensional Schr{\"o}dinger equation.

}, url = {http://stacks.iop.org/1367-2630/18/i=1/a=015010}, author = {J. Polo and A. Benseny and T. Busch and V. Ahufinger and J. Mompart} } @article {PhysRevA.91.053626, title = {Analysis beyond the Thomas-Fermi approximation of the density profiles of a miscible two-component Bose-Einstein condensate}, journal = {Phys. Rev. A}, volume = {91}, year = {2015}, month = {May}, pages = {053626}, publisher = {American Physical Society}, doi = {10.1103/PhysRevA.91.053626}, url = {http://link.aps.org/doi/10.1103/PhysRevA.91.053626}, author = {J. Polo and V. Ahufinger and P. Mason and S. Sridhar and T. P. Billam and S. A. Gardiner} } @article {93, title = {Blue-detuned optical ring trap for Bose-Einstein condensates based on conical refraction}, journal = {Optics Express}, volume = {23}, number = {2}, year = {2015}, chapter = {1638}, abstract = {We present a novel approach for the optical manipulation of neutral atoms in annular light structures produced by the phenomenon of conical refraction occurring in biaxial optical crystals. For a beam focused to a plane behind the crystal, the focal plane exhibits two concentric bright rings enclosing a ring of null intensity called the Poggendorff ring. We demonstrate both theoretically and experimentally that the Poggendorff dark ring of conical refraction is confined in three dimensions by regions of higher intensity. We derive the positions of the confining intensity maxima and minima and discuss the application of the Poggendorff ring for trapping ultra-cold atoms using the repulsive dipole force of blue-detuned light. We give analytical expressions for the trapping frequencies and potential depths along both the radial and the axial directions. Finally, we present realistic numerical simulations of the dynamics of a 87Rb Bose-Einstein condensate trapped inside the Poggendorff ring which are in good agreement with corresponding experimental results.}, keywords = {Atom optics, Birefringence, Crystal optics, Laser trapping}, url = {http://dx.doi.org/10.1364/OE.23.001638}, author = {A. Turpin and J. Polo and Yu. V. Loiko and J. K{\"u}ber and F. Schmaltz and T. K. Kalkandjiev and V. Ahufinger and G. Birkl and J. Mompart} } @article {97, title = {Coherent injecting, extracting, and velocity filtering of neutral atoms in a ring trap via spatial adiabatic passage}, journal = {European Physical Journal D}, volume = {69}, number = {6}, year = {2014}, month = {06/2014}, chapter = {147}, abstract = {We introduce a coherent technique to inject, extract, and velocity filter neutral atoms in a ring trap coupled via tunneling to two additional waveguides. By adiabatically following the transverse spatial dark state, the proposed technique allows for an efficient and robust velocity dependent atomic population transfer between the ring and the input/output waveguides. We have derived explicit conditions for the spatial adiabatic passage that depend on the atomic velocity along the input waveguide as well as on the initial population distribution among the transverse vibrational states. The validity of our proposal has been checked by numerical integration of the corresponding two-dimensional Schrodinger equation with state-of-the-art parameter values for Rb-87 atoms and an optical dipole ring trap.}, keywords = {Optics, Toroidal traps}, doi = {10.1140/epjd/e2014-40696-3}, url = {http://link.springer.com/article/10.1140/epjd/e2014-40696-3}, author = {Yu. V. Loiko and V. Ahufinger and R. Menchon-Enrich and G. Birkl and J. Mompart} } @article {98, title = {Single-atom interferometer based on two-dimensional spatial adiabatic passage}, journal = {Physical Review A}, volume = {89}, number = {5}, year = {2014}, month = {05/2014}, chapter = {053611}, abstract = {In this work, we propose a single-atom interferometer based on a fully two-dimensional spatial adiabatic passage process using a system of three identical harmonic traps in a triangular geometry. While the transfer of a single atom from the ground state of one trap to the ground state of the most distant one can successfully be achieved in a robust way for a broad range of parameter values, we point out the existence of a specific geometrical configuration of the traps for which a crossing of two energy eigenvalues occurs and the transfer of the atom fails. Instead, the wave function is robustly split into a coherent superposition between two of the traps. We show that this process can be used to construct a single-atom interferometer and discuss its performance in terms of the final population distribution among the asymptotic eigenstates of the individual traps. This interferometric scheme could be used to study space-dependent fields from ultrashort to relatively large distances, or the decay of the coherence of superposition states as a function of the distance.}, doi = {10.1103/PhysRevA.89.053611}, url = {http://dx.doi.org/10.1103/PhysRevA.89.053611}, author = {R. Menchon-Enrich and S. McEndoo and T. Busch and V. Ahufinger and J. Mompart} } @article {99, title = {Spatial adiabatic passage processes in sonic crystals with linear defects}, journal = {Physical Review B}, volume = {89}, number = {9}, year = {2014}, month = {03/2014}, chapter = {094304}, abstract = {We investigate spatial adiabatic passage processes for sound wave propagation in sonic crystals, consisting of steel cylinders embedded in a water host medium, that present two linear defects. This work constitutes an extension of the well-known quantum optical rapid adiabatic passage technique to the field of sound propagation. Several spatial adiabatic passage devices are proposed by appropriately designing the geometry of the two linear defects along the propagation direction to work as a coherent multifrequency adiabatic splitter, a phase difference analyzer, and a coherent multifrequency adiabatic coupler. These devices are robust in front of fluctuations of the geometric parameter values.}, doi = {10.1103/PhysRevB.89.094304}, url = {http://dx.doi.org/10.1103/PhysRevB.89.094304}, author = {R. Menchon-Enrich and J. Mompart and V. Ahufinger} } @article {100, title = {Tunneling-induced angular momentum for single cold atoms}, journal = {Physical Review A}, volume = {89}, number = {1}, year = {2014}, month = {01/2014}, chapter = {013626}, abstract = {We study the generation of angular momentum carrying states for a single cold particle by breaking the symmetry of a spatial adiabatic passage process in a two-dimensional system consisting of three harmonic potential wells. By following a superposition of two eigenstates of the system, a single cold particle is completely transferred to the degenerate first excited states of the final trap, which are resonantly coupled via tunneling to the ground states of the initial and middle traps. Depending on the total time of the process, angular momentum is generated in the final trap, with values that oscillate between +/-(h) over bar. This process is discussed in terms of the asymptotic eigenstates of the individual wells and the results are checked by simulations of the full twodimensional Schrodinger equation.}, doi = {10.1103/PhysRevA.89.013626}, url = {http://dx.doi.org/10.1103/PhysRevA.89.013626}, author = {R. Menchon-Enrich and S. McEndoo and J. Mompart and V. Ahufinger and T. Busch} } @article {134, title = {Light spectral filtering based on spatial adiabatic passage}, journal = {Light: Science \& Applications}, volume = {2}, year = {2013}, month = {08/2013}, chapter = {e90}, abstract = {We present the first experimental realization of a light spectral filter based on the spatial adiabatic passage technique. We demonstrate that a fully integrable CMOS-compatible system of three coupled identical total internal reflection silicon oxide waveguides with variable separation along their propagation direction can be used simultaneously as a low- and high-pass spectral filter within the visible range of wavelengths. Light is injected into the right waveguide, and after propagating along the system, long wavelengths are transferred into the left output, whereas short wavelengths propagate to the right and central outputs. The stopband reaches values up to 11 dB for the left output and approximately 20 dB for the right plus central outputs. The passband values are close to 0 dB for both cases. We also demonstrate that the filtering characteristics of the device can be controlled by modifying the parameter values, which define the geometry of the triple-waveguide system. However, the general filtering behavior of the system does not critically depend on technological variations. Thus, the spatial adiabatic passage filtering approach constitutes an alternative to other integrated filtering devices, such as interference or absorbance-based filters.}, keywords = {CMOS-compatible technology, integrated optics devices, spatial adiabatic passage, wavelength filtering devices}, doi = {doi:10.1038/lsa.2013.46}, url = {http://www.nature.com/lsa/journal/v2/n8/full/lsa201346a.html}, author = {R. Menchon-Enrich and A. Llobera and J. Vila-Planas and V. J Cadarso and J. Mompart and V. Ahufinger} } @article {126, title = {Nanoscale resolution for fluorescence microscopy via adiabatic passage}, journal = {Optics Express}, volume = {21}, number = {19}, year = {2013}, chapter = {22139}, abstract = {We propose the use of the subwavelength localization via adiabatic passage technique for fluorescence microscopy with nanoscale resolution in the far field. This technique uses a Λ-type medium coherently coupled to two laser pulses: the pump, with a node in its spatial profile, and the Stokes. The population of the Λ system is adiabatically transferred from one ground state to the other except at the node position, yielding a narrow population peak. This coherent localization allows fluorescence imaging with nanometer lateral resolution. We derive an analytical expression to asses the resolution and perform a comparison with the coherent population trapping and the stimulated-emission-depletion techniques.}, keywords = {Atomic and molecular physics, Microscopy, Quantum optics}, issn = {1094-4087}, doi = {10.1364/OE.21.022139}, url = {http://dx.doi.org/10.1364/OE.21.022139}, author = {J. L. Rubio and D. Viscor and V. Ahufinger and J. Mompart} } @article {PhysRevA.88.053628, title = {Soliton-based matter-wave interferometer}, journal = {Phys. Rev. A}, volume = {88}, year = {2013}, month = {11/2013}, pages = {053628}, publisher = {American Physical Society}, abstract = {We consider a matter-wave bright soliton interferometer composed of a harmonic potential trap with a Rosen-Morse barrier at its center on which an incident soliton collides and splits into two solitons. These two solitons recombine after a dipole oscillation in the trap at the position of the barrier. We focus on the characterization of the splitting process in the case in which the reflected and transmitted solitons have the same number of atoms. We obtain that the velocity of the split solitons strongly depends on the nonlinearity and on the width of the barrier and that the reflected soliton is in general slower than the transmitted one. Also, we study the phase difference acquired between the two solitons during the splitting and we fit semianalytically the main dependences with the velocity of the incident soliton, the nonlinearity, and the width of the barrier. The implementation of the full interferometer sequence is tested by means of the phase imprinting method.}, doi = {10.1103/PhysRevA.88.053628}, url = {http://link.aps.org/doi/10.1103/PhysRevA.88.053628}, author = {J. Polo and V. Ahufinger} } @article {140, title = {Adiabatic Passage of Light in CMOS-Compatible Silicon Oxide Integrated Rib Waveguides}, journal = {IEEE Photonics Technolopgy Letters}, volume = {24}, number = {7}, year = {2012}, month = {04/2012}, pages = {536-538}, chapter = {536}, abstract = {A fully complementary metal-oxide-semiconductor-compatible adiabatic passage of light in the visible range is presented in this letter. We experimentally show that a system of three total internal reflection waveguides, which has been defined by using non-stoichiometric silicon oxide, allows a highly efficient transfer of light between the outermost waveguides by adiabatically following one eigenmode of the system. Furthermore, we demonstrate that such transfer of light is very robust against small variations of the system parameters.}, keywords = {Adiabatic passage of light, integrated optical circuits, silicon technology, total internal reflection (TIR) waveguides}, issn = {1041-1135}, doi = {10.1109/LPT.2011.2180519}, url = {Adiabatic Passage of Light in CMOS-Compatible Silicon Oxide Integrated Rib Waveguides}, author = {R. Menchon-Enrich and A. Llobera and V. J Cadarso and J. Mompart and V. Ahufinger} } @article {PhysRevA.86.063409, title = {Single-site addressing of ultracold atoms beyond the diffraction limit via position-dependent adiabatic passage}, journal = {Phys. Rev. A}, volume = {86}, year = {2012}, month = {12/2012}, pages = {063409}, publisher = {American Physical Society}, abstract = {We propose a single-site addressing implementation based on the subwavelength localization via adiabatic passage (SLAP) technique. We consider a sample of ultracold neutral atoms loaded into a two-dimensional optical lattice with one atom per site. Each atom is modeled by a three-level Λ system in interaction with a pump and a Stokes laser pulse. Using a pump field with a node in its spatial profile, the atoms at all sites are transferred from one ground state of the system to the other via stimulated Raman adiabatic passage, except the one at the position of the node that remains in the initial ground state. This technique allows for the preparation, manipulation, and detection of atoms with a spatial resolution better than the diffraction limit, which either relaxes the requirements on the optical setup used or extends the achievable spatial resolution to lattice spacings smaller than accessible to date. In comparison to techniques based on coherent population trapping, SLAP gives a higher addressing resolution and has additional advantages such as robustness against parameter variations, coherence of the transfer process, and the absence of photon induced recoil. Additionally, the advantages of our proposal with respect to adiabatic spin-flip techniques are highlighted. Analytic expressions for the achievable addressing resolution and efficiency are derived and compared to numerical simulations for 87Rb atoms in state-of-the-art optical lattices.}, doi = {10.1103/PhysRevA.86.063409}, url = {http://link.aps.org/doi/10.1103/PhysRevA.86.063409}, author = {D. Viscor and J. L. Rubio and G. Birkl and J. Mompart and V. Ahufinger} } @article {PhysRevA.86.053827, title = {Two-color quantum memory in double-Λ media}, journal = {Phys. Rev. A}, volume = {86}, year = {2012}, month = {11/2012}, pages = {053827}, publisher = {American Physical Society}, abstract = {We propose a quantum memory for a single-photon wave packet in a superposition of two different colors, i.e., two different frequency components, using the electromagnetically induced transparency technique in a double-Λ system. We examine a specific configuration in which the two frequency components are able to exchange energy through a four-wave mixing process as they propagate, so the state of the incident photon is recovered periodically at certain positions in the medium. We investigate the propagation dynamics as a function of the relative phase between the coupling beams and the input single-photon frequency components. Moreover, by considering time-dependent coupling beams, we numerically simulate the storage and retrieval of a two-frequency-component single-photon qubit.}, doi = {10.1103/PhysRevA.86.053827}, url = {http://link.aps.org/doi/10.1103/PhysRevA.86.053827}, author = {D. Viscor and V. Ahufinger and J. Mompart and A. Zavatta and G. C. La Rocca and M. Artoni} } @article {PhysRevA.83.013605, title = {Disordered spinor Bose-Hubbard model}, journal = {Phys. Rev. A}, volume = {83}, year = {2011}, month = {Jan}, pages = {013605}, publisher = {American Physical Society}, abstract = {We study the zero-temperature phase diagram of the disordered spin-1 Bose-Hubbard model in a two-dimensional square lattice. To this aim, we use a mean-field Gutzwiller ansatz and a probabilistic mean-field perturbation theory. The spin interaction induces two different regimes, corresponding to a ferromagnetic and antiferromagnetic order. In the ferromagnetic case, the introduction of disorder reproduces analogous features of the disordered scalar Bose-Hubbard model, consisting in the formation of a Bose glass phase between Mott insulator lobes. In the antiferromagnetic regime, the phase diagram differs more from the scalar case. Disorder in the chemical potential can lead to the disappearance of Mott insulator lobes with an odd-integer filling factor and, for sufficiently strong spin coupling, to Bose glass of singlets between even-filling Mott insulator lobes. Disorder in the spinor coupling parameter results in the appearance of a Bose glass phase only between the n and the n+1 lobes for n odd. Disorder in the scalar Hubbard interaction inhibits Mott insulator regions for occupation larger than a critical value.}, doi = {10.1103/PhysRevA.83.013605}, url = {http://link.aps.org/doi/10.1103/PhysRevA.83.013605}, author = {M. Lacki and S. Paganelli and V. Ahufinger and A. Sanpera and J. Zakrzewski} } @article {PhysRevA.83.033629, title = {Filtering of matter-wave vibrational states via spatial adiabatic passage}, journal = {Phys. Rev. A}, volume = {83}, year = {2011}, month = {Mar}, pages = {033629}, publisher = {American Physical Society}, abstract = {We discuss the filtering of the vibrational states of a cold atom in an optical trap by chaining this trap with two empty ones and adiabatically controlling the tunneling. Matter-wave filtering is performed by selectively transferring the population of the highest populated vibrational state to the most distant trap while the population of the rest of the states remains in the initial trap. Analytical conditions for two-state filtering are derived and then applied to an arbitrary number of populated bound states. Realistic numerical simulations close to state-of-the-art experimental arrangements are performed by modeling the triple well with time-dependent P{\"o}schl-Teller potentials. In addition to filtering of vibrational states, we discuss applications for quantum tomography of the initial population distribution and engineering of atomic Fock states that, eventually, could be used for tunneling-assisted evaporative cooling.}, doi = {10.1103/PhysRevA.83.033629}, url = {http://link.aps.org/doi/10.1103/PhysRevA.83.033629}, author = {Yu. V. Loiko and V. Ahufinger and R. Corbal{\'a}n and G. Birkl and J. Mompart} } @article {0953-4075-44-19-195504, title = {Optical quantum memory for polarization qubits with V -type three-level atoms}, journal = {Journal of Physics B: Atomic, Molecular and Optical Physics}, volume = {44}, number = {19}, year = {2011}, pages = {195504}, abstract = {We investigate an optical quantum memory scheme with V -type three-level atoms based on the controlled reversible inhomogeneous broadening technique. We theoretically show the possibility of storing and retrieving a weak light pulse interacting with the two optical transitions of the system. This scheme implements a quantum memory for a polarization qubit{\textemdash}a single photon in an arbitrary polarization state{\textemdash}without the need of two spatially separated two-level media, thus offering the advantage of experimental compactness overcoming the limitations due to mismatching and unequal efficiencies that can arise in spatially separated memories. The effects of a relative phase change between the atomic levels, as well as of phase noise due to, for example, the presence of spurious electric and magnetic fields are analysed.}, url = {http://stacks.iop.org/0953-4075/44/i=19/a=195504}, author = {D. Viscor and A. Ferraro and Yu. V. Loiko and R. Corbal{\'a}n and J. Mompart and V. Ahufinger} } @article {PhysRevA.84.042314, title = {Quantum-state storage and processing for polarization qubits in an inhomogeneously broadened Λ-type three-level medium}, journal = {Phys. Rev. A}, volume = {84}, year = {2011}, month = {Oct}, pages = {042314}, publisher = {American Physical Society}, abstract = {We address the propagation of a single-photon pulse with two polarization components, i.e., a polarization qubit, in an inhomogeneously broadened {\textquotedblleft}phaseonium{\textquotedblright} Λ-type three-level medium. We combine some of the nontrivial propagation effects characteristic for this kind of coherently prepared systems and the controlled reversible inhomogeneous broadening technique to propose several quantum information-processing applications, such as a protocol for polarization qubit filtering and sieving as well as a tunable polarization beam splitter. Moreover, we show that by imposing a spatial variation of the atomic coherence phase, an efficient quantum memory for the incident polarization qubit can be also implemented in Λ-type three-level systems.}, doi = {10.1103/PhysRevA.84.042314}, url = {http://link.aps.org/doi/10.1103/PhysRevA.84.042314}, author = {D. Viscor and A. Ferraro and Yu. V. Loiko and J. Mompart and V. Ahufinger} } @article { ISI:000298333500005, title = {Spin Effects in Bose-Glass Phases}, journal = {Journal of Low Temperature Physics}, volume = {165}, number = {{5-6, SI}}, year = {2011}, month = {DEC}, pages = {227-238}, publisher = {{SPRINGER/PLENUM PUBLISHERS}}, address = {{233 SPRING ST, NEW YORK, NY 10013 USA}}, abstract = {We study the mechanism of formation of Bose glass (BG) phases in the spin-1 Bose Hubbard model when diagonal disorder is introduced. To this aim, we analyze first the phase diagram in the zero-hopping limit, there disorder induces superposition between Mott insulator (MI) phases with different filling numbers. Then BG appears as a compressible insulating phase (its compressibility marking the distinction with respect to a more common Mott insulator). The phase diagram for finite hopping is also calculated with the Gutzwiller approximation. The bosons{\textquoteright} spin degrees of freedom introduce another scattering channel in the two-body interaction modifying the stability of MI regions with respect to the action of disorder. This leads to some peculiar phenomena such as the creation of BG of singlets, for very strong spin correlation, or the disappearance of BG phase in some particular cases where fluctuations are not able to mix different MI regions.}, keywords = {Bose glass, Spin-1 Bose Hubbard model, Ultracold atoms}, issn = {0022-2291}, doi = {10.1007/s10909-011-0392-7}, author = {S. Paganelli and M. Lacki and V. Ahufinger and J. Zakrzewski and A. Sanpera} } @article {PhysRevA.81.043621, title = {Adiabatic splitting, transport, and self-trapping of a Bose-Einstein condensate in a double-well potential}, journal = {Phys. Rev. A}, volume = {81}, year = {2010}, month = {Apr}, pages = {043621}, publisher = {American Physical Society}, abstract = {We show that the adiabatic dynamics of a Bose-Einstein condensate (BEC) in a double-well potential can be described in terms of a dark variable resulting from the combination of the population imbalance and the spatial atomic coherence between the two wells. By means of this dark variable, we extend, to the nonlinear matter-wave case, the recent proposal by Vitanov and Shore [Phys. Rev. A 73, 053402 (2006)] on adiabatic passage techniques to coherently control the population of two internal levels of an atom or molecule. We investigate the conditions to adiabatically split or transport a BEC as well as to prepare an adiabatic self-trapping state by the optimal delayed temporal variation of the tunneling rate via either the energy bias between the two wells or the BEC nonlinearity. The emergence of nonlinear eigenstates and unstable stationary solutions of the system as well as their role in the breaking down of the adiabatic dynamics is investigated in detail.}, doi = {10.1103/PhysRevA.81.043621}, url = {http://link.aps.org/doi/10.1103/PhysRevA.81.043621}, author = {C. Ottaviani and V. Ahufinger and R. Corbal{\'a}n and J. Mompart} } @article {PhysRevA.81.033420, title = {Dipole spectrum structure of nonresonant nonpertubative driven two-level atoms}, journal = {Phys. Rev. A}, volume = {81}, year = {2010}, month = {Mar}, pages = {033420}, publisher = {American Physical Society}, abstract = {We analyze the dipole spectrum of a two-level atom excited by a nonresonant intense monochromatic field under the electric dipole approximation and beyond the rotating wave approximation. We show that the apparently complex spectral structure can be completely described by two families: harmonic frequencies of the driving field and field-induced nonlinear fluorescence. Our formulation of the problem provides quantitative laws for the most relevant spectral features: harmonic ratios and phases, nonperturbative Stark shift, and frequency limits of the harmonic plateau. In particular, we demonstrate the locking of the harmonic phases at the wings of the plateau opening the possibility of ultrashort pulse generation through harmonic filtering.}, doi = {10.1103/PhysRevA.81.033420}, url = {http://link.aps.org/doi/10.1103/PhysRevA.81.033420}, author = {A. Pic{\'o}n and L. Roso and J. Mompart and O. Varela and V. Ahufinger and R. Corbal{\'a}n and L. Plaja} } @article {PhysRevA.79.053638, title = {Coherent patterning of matter waves with subwavelength localization}, journal = {Phys. Rev. A}, volume = {79}, year = {2009}, month = {May}, pages = {053638}, publisher = {American Physical Society}, abstract = {We propose the subwavelength localization via adiabatic passage (SLAP) technique to coherently achieve state-selective patterning of matter waves well beyond the diffraction limit. The SLAP technique consists in coupling two partially overlapping and spatially structured laser fields to three internal levels of the matter wave yielding state-selective localization at those positions where the adiabatic passage process does not occur. We show that by means of this technique matter wave localization down to the single nanometer scale can be achieved. We analyze in detail the potential implementation of the SLAP technique for nanolithography with an atomic beam of metastable Ne* and for coherent patterning of a two-component R87b Bose-Einstein condensate.}, doi = {10.1103/PhysRevA.79.053638}, url = {http://link.aps.org/doi/10.1103/PhysRevA.79.053638}, author = {J. Mompart and V. Ahufinger and G. Birkl} } @article {PhysRevA.79.053809, title = {Doppler-free adiabatic self-induced transparency}, journal = {Phys. Rev. A}, volume = {79}, year = {2009}, month = {May}, pages = {053809}, publisher = {American Physical Society}, abstract = {We demonstrate that a Doppler-broadened two-level medium can be made transparent to a laser pulse by an appropriate adiabatic variation in the laser field amplitude and its nominal detuning. This technique of adiabatic self-induced transparency (ASIT) is compared with the well-known self-induced transparency phenomenon, showing that the adiabatic method is much more robust against variations in the system parameters. We also discuss a possible experimental implementation of ASIT using R87b atoms.}, doi = {10.1103/PhysRevA.79.053809}, url = {http://link.aps.org/doi/10.1103/PhysRevA.79.053809}, author = {Yu. V. Loiko and C. Serrat and R. Vilaseca and V. Ahufinger and J. Mompart and R. Corbal{\'a}n} } @article {PhysRevA.78.013608, title = {Double-barrier potentials for matter-wave gap solitons}, journal = {Phys. Rev. A}, volume = {78}, year = {2008}, month = {Jul}, pages = {013608}, publisher = {American Physical Society}, abstract = {We investigate collisions of solitons of the gap type, supported by a lattice potential in repulsive Bose-Einstein condensates, with an effective double-barrier potential that resembles a Fabry-Perot cavity. We identify conditions under which the trapping of the entire incident soliton in the cavity is possible. Collisions of the incident soliton with an earlier trapped one are considered too. In the latter case, many outcomes of the collisions are identified, including merging, release of the trapped soliton with or without being replaced by the incoming one, and trapping of both solitons.}, doi = {10.1103/PhysRevA.78.013608}, url = {http://link.aps.org/doi/10.1103/PhysRevA.78.013608}, author = {V. Ahufinger and B. A. Malomed and G. Birkl and R. Corbal{\'a}n and A. Sanpera} } @article {1367-2630-9-1-004, title = {Quantum switches and quantum memories for matter-wave lattice solitons}, journal = {New Journal of Physics}, volume = {9}, number = {1}, year = {2007}, pages = {4}, abstract = {We study the possibility of implementing a quantum switch and a quantum memory using matter-wave lattice solitons and making them interact with {\textquoteright}effective{\textquoteright} potentials (barrier/well) corresponding to defects of the optical lattice. In the case of interaction with an {\textquoteright}effective{\textquoteright} potential barrier, the bright lattice soliton experiences an abrupt transition from complete transmission to complete reflection (quantum switch) for a critical height of the barrier. The trapping of the soliton in an {\textquoteright}effective{\textquoteright} potential well and its release on demand, without losses, shows the feasibility of using the system as a quantum memory. The inclusion of defects as a way of controlling the interactions between two solitons is also reported.}, url = {http://stacks.iop.org/1367-2630/9/i=1/a=004}, author = {V. Ahufinger and A Mebrahtu and R. Corbal{\'a}n and A. Sanpera} } @article {PhysRevLett.98.023003, title = {Trapped Ion Chain as a Neural Network: Error Resistant Quantum Computation}, journal = {Phys. Rev. Lett.}, volume = {98}, year = {2007}, month = {Jan}, pages = {023003}, publisher = {American Physical Society}, abstract = {We demonstrate the possibility of realizing a neural network in a chain of trapped ions with induced long range interactions. Such models permit one to store information distributed over the whole system. The storage capacity of such a network, which depends on the phonon spectrum of the system, can be controlled by changing the external trapping potential. We analyze the implementation of error resistant universal quantum information processing in such systems.}, doi = {10.1103/PhysRevLett.98.023003}, url = {http://link.aps.org/doi/10.1103/PhysRevLett.98.023003}, author = {M. Pons and V. Ahufinger and C. Wunderlich and A. Sanpera and S. Braungardt and A. Sen(De) and U. Sen and M. Lewenstein} } @article { ISI:000246721000001, title = {Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond}, journal = {Advances in Physics}, volume = {56}, number = {2}, year = {2007}, pages = {243-379}, publisher = {{TAYLOR \& FRANCIS LTD}}, address = {{4 PARK SQUARE, MILTON PARK, ABINGDON OX14 4RN, OXON, ENGLAND}}, abstract = {We review recent developments in the physics of ultracold atomic and molecular gases in optical lattices. Such systems are nearly perfect realisations of various kinds of Hubbard models, and as such may very well serve to mimic condensed matter phenomena. We show how these systems may be employed as quantum simulators to answer some challenging open questions of condensed matter, and even high energy physics. After a short presentation of the models and the methods of treatment of such systems, we discuss in detail, which challenges of condensed matter physics can be addressed with (i) disordered ultracold lattice gases, (ii) frustrated ultracold gases, (iii) spinor lattice gases, (iv) lattice gases in {\textquoteleft}{\textquoteleft}artificial{\textquoteright}{\textquoteright} magnetic fields, and, last but not least, (v) quantum information processing in lattice gases. For completeness, also some recent progress related to the above topics with trapped cold gases will be discussed.}, keywords = {disordered systems, frustrated systems, Hubbard models, quantum information, spinor gases, Ultracold atomic and molecular gases}, issn = {0001-8732}, doi = {10.1080/00018730701223200}, author = {M. Lewenstein and A. Sanpera and V. Ahufinger and B. Damski and A. Sen(De) and U. Sen} } @article {PhysRevA.75.023801, title = {Ultrashort pulse control of space-dependent excitations in a three-level system}, journal = {Phys. Rev. A}, volume = {75}, year = {2007}, month = {Feb}, pages = {023801}, publisher = {American Physical Society}, abstract = {Coherent control of regions with spatial excitation of populations and coherence between two lower states in three-level Λ-type quantum systems mediated by the self-induced transparency (SIT) phenomenon is theoretically investigated with one- and two-color ultrashort pulses and with pulse sequences beyond the slowly varying envelope (SVEA) and rotating wave (RWA) approximations. The effects of different parameters characterizing the pulses and the medium on the location as well as the width of such excited regions have been studied numerically by means of the finite-difference time-domain (FDTD) method. It has been determined that with a scheme of two-pulse excitation one can effectively control the position at which the region is written and its width. In particular, the position of the excited region can be controlled by the area of the pulses. We find that the maximum value of the population transferred to the lower excited state depends on the detuning of the pulses with respect to the one-photon resonances, and that both position and width of the region also depend on the temporal duration of the pulses. We show how after the excited region is written, its position can be shifted by additional pulses. On the basis of numerical results, scaling laws are formulated for the reported phenomena. With such control, the width of the region excited inside the medium can be reduced to the order of the wavelength of the light.}, doi = {10.1103/PhysRevA.75.023801}, url = {http://link.aps.org/doi/10.1103/PhysRevA.75.023801}, author = {Yu. V. Loiko and C. Serrat and R. Vilaseca and V. Ahufinger and J. Mompart and R. Corbal{\'a}n} } @article {PhysRevA.74.062309, title = {Quantum-information processing in disordered and complex quantum systems}, journal = {Phys. Rev. A}, volume = {74}, year = {2006}, month = {Dec}, pages = {062309}, publisher = {American Physical Society}, abstract = {We study quantum information processing in complex disordered many body systems that can be implemented by using lattices of ultracold atomic gases and trapped ions. We demonstrate, first in the short range case, the generation of entanglement and the local realization of quantum gates in a disordered magnetic model describing a quantum spin glass. We show that in this case it is possible to achieve fidelities of quantum gates higher than in the classical case. Complex systems with long range interactions, such as ions chains or dipolar atomic gases, can be used to model neural network Hamiltonians. For such systems, where both long range interactions and disorder appear, it is possible to generate long range bipartite entanglement. We provide an efficient analytical method to calculate the time evolution of a given initial state, which in turn allows us to calculate its quantum correlations.}, doi = {10.1103/PhysRevA.74.062309}, url = {http://link.aps.org/doi/10.1103/PhysRevA.74.062309}, author = {A. Sen(De) and U. Sen and V. Ahufinger and H. J. Briegel and A. Sanpera and M. Lewenstein} } @article {0953-4075-39-10-S12, title = {Strongly correlated Fermi{\textendash}Bose mixtures in disordered optical lattices}, journal = {Journal of Physics B: Atomic, Molecular and Optical Physics}, volume = {39}, number = {10}, year = {2006}, pages = {S121}, abstract = {We investigate theoretically the low-temperature physics of a two-component ultracold mixture of bosons and fermions in disordered optical lattices. We focus on the strongly correlated regime. We show that, under specific conditions, composite fermions, made of one fermion plus one bosonic hole, form. The composite picture is used to derive an effective Hamiltonian whose parameters can be controlled via the boson{\textendash}boson and the boson{\textendash}fermion interactions, the tunnelling terms and the inhomogeneities. We finally investigate the quantum phase diagram of the composite fermions and show that it corresponds to the formation of Fermi glasses, spin glasses and quantum percolation regimes.}, url = {http://stacks.iop.org/0953-4075/39/i=10/a=S12}, author = {L. Sanchez-Palencia and V. Ahufinger and A. Kantian and J. Zakrzewski and A. Sanpera and M. Lewenstein} } @conference { ISI:000236853300016, title = {Disordered complex systems using cold gases and trapped ions}, booktitle = {Laser Spectroscopy}, year = {2005}, note = {{17th International Conference on Laser Spectroscopy, Aviemore, SCOTLAND, JUN 19-24, 2005}}, pages = {{158-166}}, type = {{Proceedings Paper}}, address = {PO BOX 128 FARRER RD, SINGAPORE 9128, SINGAPORE}, abstract = {We report our research on disordered complex systems using cold gases and trapped ions and address the possibility of using complex systems for quantum information processing. Two simple paradigmatic models of disordered complex systems are here revisited. The first one corresponds to a short range disordered Ising Hamiltonian (spin glasses) which can be implemented with a bose-fermi (bose-bose) mixture in a disordered optical lattice. The second model we address here is a long range disordered Hamiltonian characteristic of neural networks (Hopfield model) which can be implemented in a chain of trapped ions with appropriately designed interactions.}, isbn = {981-256-659-7}, author = {A. Sen(De) and U. Sen and M. Lewenstein and V. Ahufinger and M. Pons and A. Sanpera}, editor = {E. A. Hinds and A. Ferguson and E. Riis} } @article {PhysRevA.72.063616, title = {Disordered ultracold atomic gases in optical lattices: A case study of Fermi-Bose mixtures}, journal = {Phys. Rev. A}, volume = {72}, year = {2005}, month = {Dec}, pages = {063616}, publisher = {American Physical Society}, abstract = {We present a review of properties of ultracold atomic Fermi-Bose mixtures in inhomogeneous and random optical lattices. In the strong interacting limit and at very low temperatures, fermions form, together with bosons or bosonic holes, composite fermions. Composite fermions behave as a spinless interacting Fermi gas, and in the presence of local disorder they interact via random couplings and feel effective random local potential. This opens a wide variety of possibilities of realizing various kinds of ultracold quantum disordered systems. In this paper we review these possibilities, discuss the accessible quantum disordered phases, and methods for their detection. The discussed quantum phases include Fermi glasses, quantum spin glasses, {\textquotedblleft}dirty{\textquotedblright} superfluids, disordered metallic phases, and phases involving quantum percolation.}, doi = {10.1103/PhysRevA.72.063616}, url = {http://link.aps.org/doi/10.1103/PhysRevA.72.063616}, author = {V. Ahufinger and L. Sanchez-Palencia and A. Kantian and A. Sanpera and M. Lewenstein} } @article { ISI:000225524900010, title = {Frequency up-conversion He-Ne laser without inversion}, journal = {Applied Physics B-Lasers and Optics}, volume = {80}, number = {1}, year = {2005}, month = {JAN}, pages = {67-72}, publisher = {{SPRINGER}}, address = {{233 SPRING STREET, NEW YORK, NY 10013 USA}}, abstract = {{A scheme for obtaining up-conversion lasing without inversion in the visible range is proposed using a Doppler-broadened He-Ne mixture as active medium. We consider a cascade scheme (2s(2) <{\textendash}{\textendash}> 2p(2) <{\textendash}{\textendash}> 1s(3)) with a frequency upconversion ratio of 1.91. The upper transition is inverted and driven by an external field and lasing without inversion occurs at 616.4 nm provided that the collisional decay rates of the 1s(3) and 1s(5) levels overcome a certain threshold.}}, issn = {0946-2171}, doi = {10.1007/s00340-004-1694-0}, author = {V. Ahufinger and R Shuker and R. Corbal{\'a}n} } @article {PhysRevLett.94.130403, title = {Lattice Solitons in Quasicondensates}, journal = {Phys. Rev. Lett.}, volume = {94}, year = {2005}, month = {Apr}, pages = {130403}, publisher = {American Physical Society}, abstract = {We analyze finite temperature effects in the generation of bright solitons in condensates in optical lattices. We show that even in the presence of strong phase fluctuations solitonic structures with a well defined phase profile can be created. We propose a novel family of variational functions which describe well the properties of these solitons and account for the nonlinear effects in the band structure. We discuss also the mobility and collisions of these localized wave packets.}, doi = {10.1103/PhysRevLett.94.130403}, url = {http://link.aps.org/doi/10.1103/PhysRevLett.94.130403}, author = {V. Ahufinger and A. Sanpera} } @article {PhysRevA.69.053604, title = {Creation and mobility of discrete solitons in Bose-Einstein condensates}, journal = {Phys. Rev. A}, volume = {69}, year = {2004}, month = {May}, pages = {053604}, publisher = {American Physical Society}, abstract = {We analyze the generation and mobility of discrete solitons in Bose-Einstein condensates confined in an optical lattice under realistic experimental conditions. We discuss first the creation of one-dimensional discrete solitons, for both attractive and repulsive interatomic interactions. We then address the issue of their mobility, focusing our attention on the conditions for the experimental observability of the Peierls-Nabarro barrier. Finally we report on the generation of self-trapped structures in two and three dimensions. Discrete solitons may open alternative routes for the manipulation and transport of Bose-Einstein condensates.}, doi = {10.1103/PhysRevA.69.053604}, url = {http://link.aps.org/doi/10.1103/PhysRevA.69.053604}, author = {V. Ahufinger and A. Sanpera and P. Pedri and L. Santos and M. Lewenstein} } @article {PhysRevLett.91.083901, title = {Cavity Solitons in Two-Level Lasers with Dense Amplifying Medium}, journal = {Phys. Rev. Lett.}, volume = {91}, year = {2003}, month = {Aug}, pages = {083901}, publisher = {American Physical Society}, abstract = {Local-field effects are known to induce bistability in dense optical media. We examine theoretically whether this property is preserved in broad-area cavities, and show that bistability between the homogeneous lasing and nonlasing states of the system persists provided a Fourier filtering technique is used to prevent off-axis emission. The resulting bistability gives rise to spatial light localization in the form of cavity solitons, which exhibit a particularly large degree of plasticity as a function of the characteristics of the addressing beam. This is the simplest laser able to sustain cavity solitons.}, doi = {10.1103/PhysRevLett.91.083901}, url = {http://link.aps.org/doi/10.1103/PhysRevLett.91.083901}, author = {V. Ahufinger and J. Garc{\'\i}a-Ojalvo and J. Mompart and M. C. Torrent and R. Corbal{\'a}n and R. Vilaseca} } @article {1464-4266-5-3-301, title = {Enlargement of the inversionless lasing domain by using broad-area cavities}, journal = {Journal of Optics B: Quantum and Semiclassical Optics}, volume = {5}, number = {3}, year = {2003}, pages = {201}, abstract = {We investigate analytically and numerically the role of diffraction in the operation of a broad-area inversionless laser in a cascade three-level configuration. Through a linear stability analysis of the trivial non-lasing solution and numerical integration of the corresponding Maxwell{\textendash}Schr{\"o}dinger equations, we show that off-axis emission allows stationary inversionless lasing over a cavity detuning range much larger than in small-aspect-ratio cavities and in conventionally inverted three-level lasers. In addition, we investigate inversionless lasing in a self-pulsing regime in the presence of diffraction, which leads to rich spatiotemporal dynamics.}, url = {http://stacks.iop.org/1464-4266/5/i=3/a=301}, author = {J. Mompart and M. C. Torrent and V. Ahufinger and J. Garc{\'\i}a-Ojalvo and R. Corbal{\'a}n and R. Vilaseca} } @article {1464-4266-5-3-311, title = {Gain without inversion at two symmetrical sidebands of resonance in cold free 87 Rb atoms: an experimental proposal}, journal = {Journal of Optics B: Quantum and Semiclassical Optics}, volume = {5}, number = {3}, year = {2003}, pages = {268}, abstract = {We propose an experiment for obtaining about 0.4\% inversionless gain at the sidebands of resonance in cold free 87 Rb atoms. This gain is of the same order of magnitude as the one already observed near resonance (Kitching and Hollberg 1999 Phys. Rev. A 59 4685).}, url = {http://stacks.iop.org/1464-4266/5/i=3/a=311}, author = {V. Ahufinger and R. Corbal{\'a}n} } @article {Ahufinger2002159, title = {Electromagnetically induced transparency in a Bose{\textendash}Einstein condensate}, journal = {Optics Communications}, volume = {211}, number = {1{\textendash}6}, year = {2002}, pages = {159 - 165}, abstract = {We report on the direct observation of the electromagnetically induced transparency (EIT) lineshape of cold 87Rb atoms above and below the transition temperature for Bose{\textendash}Einstein condensation (BEC). Similar results are observed in both temperature regimes, with an absorption reduction of about 60\%. Good agreement with a theoretical model is discussed.}, issn = {0030-4018}, doi = {http://dx.doi.org/10.1016/S0030-4018(02)01826-6}, url = {http://www.sciencedirect.com/science/article/pii/S0030401802018266}, author = {V. Ahufinger and R. Corbal{\'a}n and F. Cataliotti and S. Burger and F. Minardi and C. Fort} } @article {PhysRevA.64.033802, title = {Electromagnetically induced transparency with a standing-wave drive in the frequency up-conversion regime}, journal = {Phys. Rev. A}, volume = {64}, year = {2001}, month = {Aug}, pages = {033802}, publisher = {American Physical Society}, abstract = {We study electromagnetically induced transparency for a probe traveling-wave (TW) laser field in closed Doppler-broadened three-level systems driven by a standing-wave (SW) laser field of moderate intensity (its Rabi frequencies are smaller than the Doppler width of the driven transition). We show that probe windows of transparency occur for values of the probe to drive field frequency ratio R close to half-integer values. For optical transitions and typical values of Doppler broadening for atoms in a vapor cell, we show that for R>1 a SW drive field is appreciably more efficient than a TW drive in inducing probe transparency. As examples, we consider parameters for real cascade schemes in barium atoms with R≈1.5 and in beryllium atoms with R≈3.5 showing that probe transmission values well above 50\% are possible for conditions in which it is almost negligible either without driving field or with only one of the TW components of the drive. We show that a strongly asymmetric drive having two TW components with unequal intensities is even more eficient than a symmetric SW drive in inducing probe transparency. The case of arbitrary probe intensity is also considered.}, doi = {10.1103/PhysRevA.64.033802}, url = {http://link.aps.org/doi/10.1103/PhysRevA.64.033802}, author = {F. Silva and J. Mompart and V. Ahufinger and R. Corbal{\'a}n} } @article {0295-5075-51-3-286, title = {Electromagnetically induced transparency in Doppler-broadened three-level systems with resonant standing-wave drive}, journal = {EPL (Europhysics Letters)}, volume = {51}, number = {3}, year = {2000}, pages = {286}, abstract = {We study electromagnetically induced transparency for a probe travelling-wave (TW) laser field in closed Doppler-broadened three-level systems driven by a resonant standing-wave (SW) laser field of moderate intensity (its Rabi frequencies are smaller than the Doppler width of the driven transition). We show that probe windows of transparency occur only for values of the probe-to-drive field frequency ratio R close to half-integer values. For optical transitions and typical values of Doppler broadening for atoms in a vapor cell, we show that for R > 1 a SW drive field is appreciably more efficient than a TW driving in inducing probe transparency. As an example, we consider parameters for a real closed cascade scheme in barium atoms with R $\#$$\#$IMG$\#$$\#$ [http://ej.iop.org/icons/Entities/simeq.gif] {simeq} 1.5 showing that probe transmission values of 50\% are possible for cases in which the transmission is almost negligible either without driving field or with only one of the TW components of the drive.}, url = {http://stacks.iop.org/0295-5075/51/i=3/a=286}, author = {F. Silva and J. Mompart and V. Ahufinger and R. Corbal{\'a}n} } @article {PhysRevA.61.053814, title = {Lasing without inversion in three-level systems without external coherent driving}, journal = {Phys. Rev. A}, volume = {61}, year = {2000}, month = {Apr}, pages = {053814}, publisher = {American Physical Society}, abstract = {We have studied an incoherently pumped laser operating with a Doppler-broadened three-level system placed in a doubly resonant cavity. This system generates two laser fields, one of them without population inversion. Both ladder and V-type three-level schemes are considered with a ratio R=ωα/ωβ of inversionless laser frequency ωα to ordinary laser frequency ωβ of R=0.67 and R=1.88, respectively. Dual-wavelength lasing extends up to Doppler-broadening values for optical transitions of atoms in a vapor cell. Some considerations for the practical realization of this dual-wavelength laser are discussed.}, doi = {10.1103/PhysRevA.61.053814}, url = {http://link.aps.org/doi/10.1103/PhysRevA.61.053814}, author = {V. Ahufinger and J. Mompart and R. Corbal{\'a}n} } @article {1464-4266-2-3-321, title = {Propagation effects on lasing without population inversion}, journal = {Journal of Optics B: Quantum and Semiclassical Optics}, volume = {2}, number = {3}, year = {2000}, pages = {359}, abstract = {We study propagation effects on lasing without population inversion in a Doppler-broadened V -type three-level system. In particular, we focus our analysis on frequency up-conversion lasing without inversion in atomic rubidium. In an atomic beam configuration, we show that it is possible to increase notably the probe gain per single pass through the active medium by detuning driving and probe fields out of one-photon resonance but maintaining the two-photon resonance condition. In a vapour cell configuration, we show that due to propagation effects the probe gain per single pass depends strongly on the driving field intensity at the entrance of the active medium. In fact, for appropriate parameter values, it is possible to reach values of the probe gain per single pass of around 40\%. For this last case, we have considered the feedback of a ring laser cavity.}, url = {http://stacks.iop.org/1464-4266/2/i=3/a=321}, author = {J. Mompart and V. Ahufinger and R. Corbal{\'a}n and F Prati} } @article { ISI:000082230000013, title = {Inversionless amplification with standing-wave drive}, journal = {Laser Physics}, volume = {9}, number = {4}, year = {1999}, month = {JUL-AUG}, pages = {858-865}, publisher = {{INTERPERIODICA}}, address = {{PO BOX 1831, BIRMINGHAM, AL 35201-1831 USA}}, abstract = {We study amplification without inversion in closed Doppler-broadened three-level systems driven by a standing-wave (SW) laser field. Our results are compared to those of the well-known case of a traveling-wave drive. A distinguishing feature of the SW case is the contribution to probe the gain of multiphoton processes involving one probe photon and several pump photons, with alternating absorption and emission from the two counterpropagating pump components. These processes are only weakly affected by Doppler broadening for probe to drive frequency ratios R equal to integer numbers. Examples of inversionless amplification with frequency up-conversion ratios R = 3 and R = 4 are presented.}, issn = {1054-660X}, author = {F. Silva and V. Ahufinger and J. Mompart and R. Corbal{\'a}n} } @article {PhysRevA.60.614, title = {Lasing without inversion with frequency up-conversion in a Doppler-broadened V-type three-level system}, journal = {Phys. Rev. A}, volume = {60}, year = {1999}, month = {Jul}, pages = {614{\textendash}620}, publisher = {American Physical Society}, abstract = {We study lasing without inversion in a Doppler-broadened V-type three-level system in the frequency up-conversion regime. We show that the ratio R=ωl/ωd of generated laser frequency to driving laser frequency that can be achieved using a vapor cell is modest (R<~2). Our analysis demonstrates that using an atomic beam the frequency of the generated field can be substantially larger than that of the driving field R\~{}10. Two different configurations are considered: (a) copropagating driving and laser beams orthogonal to the atomic beam, and (b) counterpropagating driving and atomic beams and laser beam at a determined angle with the driving beam.}, doi = {10.1103/PhysRevA.60.614}, url = {http://link.aps.org/doi/10.1103/PhysRevA.60.614}, author = {V. Ahufinger and J. Mompart and R. Corbal{\'a}n} } @article { ISI:000082230000012, title = {Quantum interference and quantum-Zeno effect in amplification without inversion}, journal = {Laser Physics}, volume = {9}, number = {9}, year = {1999}, month = {JUL-AUG}, pages = {844-857}, publisher = {{INTERPERIODICA}}, address = {{PO BOX 1831, BIRMINGHAM, AL 35201-1831 USA}}, abstract = {We analyze amplification without inversion (AWI) in different homogeneously broadened closed three-level systems in the framework of both density-matrix and quantum-jump formalisms. With the density-matrix formalism we study the nature of quantum interference in these systems; determine analytically the condition for AWI and locate the position of maxima and minima in the probe absorption spectrum. Within the quantum-jump formalism we calculate the relative probabilities of the various physical processes responsible for probe field amplification and absorption, and analyze the role of the quantum-Zeno effect in AWI. The result is that AWI in the h and p schemes is due to one-photon processes while for V and Lambda schemes are due to two-photon processes. We also show that AWI in V and h schemes always occurs in the quantum-Zeno regime, while this regime is not necessary for AWI in the Lambda and p schemes.}, issn = {1054-660X}, author = {J. Mompart and V. Ahufinger and F. Silva and R. Corbal{\'a}n and R. Vilaseca} }