We study the random walk of a particle in a compartmentalized environment, as realized in biological samples or solid state compounds. Each compartment is characterized by its length L and the boundaries transmittance T. We identify two relevant spatio-temporal scales that provide alternative descriptions of the dynamics: (i) the microscale, in which the particle position is monitored at constant time intervals; and (ii) the mesoscale, in which it is monitored only when the particle crosses a boundary between compartments. Both descriptions provide—by construction—the same long time behavior. The analytical description obtained at the proposed mesoscale allows for a complete characterization of the complex movement at the microscale, thus representing a fruitful approach for this kind of systems. We show that the presence of disorder in the transmittance is a necessary condition to induce anomalous diffusion, whereas the spatial heterogeneity reduces the degree of subdiffusion and, in some cases, can even compensate for the disorder induced by the stochastic transmittance.

%B Frontiers in Physics %V 7 %P 31 %U https://www.frontiersin.org/article/10.3389/fphy.2019.00031 %R 10.3389/fphy.2019.00031 %0 Journal Article %J Nature Photonics %D 2019 %T Knotting fractional-order knots with the polarization state of light %A E. Pisanty %A G. J. Machado %A V. Vicuña-Hernández %A A. Picón %A A. Celi %A J. P. Torres %A M. Lewenstein %XThe fundamental polarization singularities of monochromatic light are normally associated with invariance under coordinated rotations: symmetry operations that rotate the spatial dependence of an electromagnetic field by an angle *θ* and its polarization by a multiple *γθ* of that angle. These symmetries are generated by mixed angular momenta of the form *J*_{γ} = *L* + *γS*, and they generally induce Möbius-strip topologies, with the coordination parameter *γ* restricted to integer and half-integer values. In this work we construct beams of light that are invariant under coordinated rotations for arbitrary rational *γ*, by exploiting the higher internal symmetry of ‘bicircular’ superpositions of counter-rotating circularly polarized beams at different frequencies. We show that these beams have the topology of a torus knot, which reflects the subgroup generated by the torus-knot angular momentum *J*_{γ}, and we characterize the resulting optical polarization singularity using third- and higher-order field moment tensors, which we experimentally observe using nonlinear polarization tomography.

The year 2015 was the International Year of Light. However, it also marked, the 20th anniversary of the first observation of Bose–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 ‘Quantum Optics in the International Year of Light’ 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 ‘Ultracold atoms in optical lattices: Simulating quantum many-body systems’ (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—the present essay is therefore upgraded to include the latest developments.

%B Physica Scripta %V 92 %P 013003 %U http://stacks.iop.org/1402-4896/92/i=1/a=013003 %0 Journal Article %J Phys. Rev. A %D 2017 %T Single-atom edgelike states via quantum interference %A G. Pelegrí %A J. Polo %A A. Turpin %A M. Lewenstein %A J. Mompart %A V. Ahufinger %XWe 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.

%B Phys. Rev. A %V 95 %P 013614 %8 Jan %U http://link.aps.org/doi/10.1103/PhysRevA.95.013614 %R 10.1103/PhysRevA.95.013614 %0 Journal Article %J Phys. Rev. Lett. %D 2007 %T Trapped Ion Chain as a Neural Network: Error Resistant Quantum Computation %A M. Pons %A V. Ahufinger %A C. Wunderlich %A A. Sanpera %A S. Braungardt %A A. Sen(De) %A U. Sen %A M. Lewenstein %X 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. %B Phys. Rev. Lett. %I American Physical Society %V 98 %P 023003 %8 Jan %U http://link.aps.org/doi/10.1103/PhysRevLett.98.023003 %R 10.1103/PhysRevLett.98.023003 %0 Journal Article %J Advances in Physics %D 2007 %T Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond %A M. Lewenstein %A A. Sanpera %A V. Ahufinger %A B. Damski %A A. Sen(De) %A U. Sen %K disordered systems %K frustrated systems %K Hubbard models %K quantum information %K spinor gases %K Ultracold atomic and molecular gases %X 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 ``artificial'' 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. %B Advances in Physics %I {TAYLOR & FRANCIS LTD} %C {4 PARK SQUARE, MILTON PARK, ABINGDON OX14 4RN, OXON, ENGLAND} %V 56 %P 243-379 %R 10.1080/00018730701223200 %0 Journal Article %J Phys. Rev. A %D 2006 %T Quantum-information processing in disordered and complex quantum systems %A A. Sen(De) %A U. Sen %A V. Ahufinger %A H. J. Briegel %A A. Sanpera %A M. Lewenstein %X 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. %B Phys. Rev. A %I American Physical Society %V 74 %P 062309 %8 Dec %U http://link.aps.org/doi/10.1103/PhysRevA.74.062309 %R 10.1103/PhysRevA.74.062309 %0 Journal Article %J Journal of Physics B: Atomic, Molecular and Optical Physics %D 2006 %T Strongly correlated Fermi–Bose mixtures in disordered optical lattices %A L. Sanchez-Palencia %A V. Ahufinger %A A. Kantian %A J. Zakrzewski %A A. Sanpera %A M. Lewenstein %X 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–boson and the boson–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. %B Journal of Physics B: Atomic, Molecular and Optical Physics %V 39 %P S121 %U http://stacks.iop.org/0953-4075/39/i=10/a=S12 %0 Journal Article %J Optics Communications %D 2006 %T Three level atom optics in dipole traps and waveguides %A K. Eckert %A J. Mompart %A R. Corbalán %A M. Lewenstein %A G. Birkl %X An analogy is explored between a setup of three atomic traps coupled via tunneling and an internal atomic three-level system interacting with two laser fields. Within this scenario we describe a \{STIRAP\} like process which allows to move an atom between the ground states of two trapping potentials and analyze its robustness. This analogy is extended to other robust and coherent transport schemes and to systems of more than a single atom. Finally it is applied to manipulate external degrees of freedom of atomic wave packets propagating in waveguides. %B Optics Communications %V 264 %P 264 - 270 %U http://www.sciencedirect.com/science/article/pii/S003040180600486X %R http://dx.doi.org/10.1016/j.optcom.2006.02.056 %0 Conference Paper %B Laser Spectroscopy %D 2005 %T Disordered complex systems using cold gases and trapped ions %A A. Sen(De) %A U. Sen %A M. Lewenstein %A V. Ahufinger %A M. Pons %A A. Sanpera %E E. A. Hinds %E A. Ferguson %E E. Riis %X 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. %B Laser Spectroscopy %C PO BOX 128 FARRER RD, SINGAPORE 9128, SINGAPORE %P {158-166} %@ 981-256-659-7 %9 {Proceedings Paper} %0 Journal Article %J Phys. Rev. A %D 2005 %T Disordered ultracold atomic gases in optical lattices: A case study of Fermi-Bose mixtures %A V. Ahufinger %A L. Sanchez-Palencia %A A. Kantian %A A. Sanpera %A M. Lewenstein %X 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, “dirty” superfluids, disordered metallic phases, and phases involving quantum percolation. %B Phys. Rev. A %I American Physical Society %V 72 %P 063616 %8 Dec %U http://link.aps.org/doi/10.1103/PhysRevA.72.063616 %R 10.1103/PhysRevA.72.063616 %0 Book Section %B Quantum Information Processing %D 2005 %T Entanglement Properties of Composite Quantum Systems %A K. Eckert %A O. Guehne %A F. Hulpke %A P. Hyllus %A J. Korbicz %A J. Mompart %A D. Bruss %A M. Lewenstein %A A. Sanpera %E T. Beth %E G. Leuchs %X We present here an overview of our work concerning entanglement properties of composite quantum systems. The characterization of entanglement, i.e. the possibility to assert if a given quantum state is entangled with others and how much entangled it is, remains one of the most fundamental open questions in quantum information theory. We discuss our recent results related to the problem of separability and distillability for distinguishable particles, employing the tool of witness operators. Finally, we also state our results concerning quantum correlations for indistinguishable particles. %B Quantum Information Processing %I BLACKWELL SCIENCE PUBL %C OSNEY MEAD, OXFORD OX2 0EL, ENGLAND %P 83-99 %@ 978-3-52760-600-9 %9 {Article; Book Chapter} %R 10.1002/3527606009.ch7 %0 Journal Article %J Phys. Rev. A %D 2005 %T One- and two-dimensional quantum walks in arrays of optical traps %A K. Eckert %A J. Mompart %A G. Birkl %A M. Lewenstein %X We propose a different implementation of discrete-time quantum walks for a neutral atom in an array of optical microtraps or an optical lattice. We analyze a one-dimensional walk in position space, with the coin, the additional qubit degree of freedom that controls the displacement of the quantum walker, implemented as a spatially delocalized qubit, i.e., the coin is also encoded in position space. We analyze the dependence of the quantum walk on temperature and experimental imperfections such as shaking in the trap positions. Finally, combining a spatially delocalized qubit and a hyperfine qubit, we also give a scheme to realize a quantum walk on a two-dimensional square lattice with the possibility of implementing different coin operators. %B Phys. Rev. A %I American Physical Society %V 72 %P 012327 %8 Jul %U http://link.aps.org/doi/10.1103/PhysRevA.72.012327 %R 10.1103/PhysRevA.72.012327 %0 Journal Article %J Phys. Rev. A %D 2004 %T Creation and mobility of discrete solitons in Bose-Einstein condensates %A V. Ahufinger %A A. Sanpera %A P. Pedri %A L. Santos %A M. Lewenstein %X 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. %B Phys. Rev. A %I American Physical Society %V 69 %P 053604 %8 May %U http://link.aps.org/doi/10.1103/PhysRevA.69.053604 %R 10.1103/PhysRevA.69.053604 %0 Journal Article %J Phys. Rev. A %D 2004 %T Three-level atom optics via the tunneling interaction %A K. Eckert %A M. Lewenstein %A R. Corbalán %A G. Birkl %A W. Ertmer %A J. Mompart %X Three-level atom optics is introduced as a simple, efficient, and robust method to coherently manipulate and transport neutral atoms. The tunneling interaction among three trapped states allows us to realize the spatial analog of the stimulated Raman adiabatic passage, coherent population trapping, and electromagnetically induced transparency techniques and offers a wide range of possible applications. We investigate an implementation in optical microtrap arrays and show that under realistic parameters the coherent manipulation and transfer of neutral atoms among dipole traps could be realized in the millisecond range. %B Phys. Rev. A %I American Physical Society %V 70 %P 023606 %8 Aug %U http://link.aps.org/doi/10.1103/PhysRevA.70.023606 %R 10.1103/PhysRevA.70.023606 %0 Journal Article %J Phys. Rev. Lett. %D 2003 %T Quantum Computing with Spatially Delocalized Qubits %A J. Mompart %A K. Eckert %A W. Ertmer %A G. Birkl %A M. Lewenstein %X We analyze the operation of quantum gates for neutral atoms with qubits that are delocalized in space, i.e., the computational basis states are defined by the presence of a neutral atom in the ground state of one out of two trapping potentials. The implementation of single-qubit gates as well as a controlled phase gate between two qubits is discussed and explicit calculations are presented for rubidium atoms in optical microtraps. Furthermore, we show how multiqubit highly entangled states can be created in this scheme. %B Phys. Rev. Lett. %I American Physical Society %V 90 %P 147901 %8 Apr %U http://link.aps.org/doi/10.1103/PhysRevLett.90.147901 %R 10.1103/PhysRevLett.90.147901 %0 Journal Article %J Phys. Rev. A %D 2002 %T Quantum computing in optical microtraps based on the motional states of neutral atoms %A K. Eckert %A J. Mompart %A X. X. Yi %A J. Schliemann %A D. Bruss %A G. Birkl %A M. Lewenstein %X We investigate quantum computation with neutral atoms in optical microtraps where the qubit is implemented in the motional states of the atoms, i.e., in the two lowest vibrational states of each trap. The quantum gate operation is performed by adiabatically approaching two traps and allowing tunneling and cold collisions to take place. We demonstrate the capability of this scheme to realize a square root of swap gate, and address the problem of double occupation and excitation to other unwanted states. We expand the two-particle wave function in an orthonormal basis and analyze quantum correlations throughout the whole gate process. Fidelity of the gate operation is evaluated as a function of the degree of adiabaticity in moving the traps. Simulations are based on rubidium atoms in state-of-the-art optical microtraps with quantum gate realizations in the few tens of milliseconds duration range. %B Phys. Rev. A %I American Physical Society %V 66 %P 042317 %8 Oct %U http://link.aps.org/doi/10.1103/PhysRevA.66.042317 %R 10.1103/PhysRevA.66.042317