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 2011 %T Disordered spinor Bose-Hubbard model %A M. Lacki %A S. Paganelli %A V. Ahufinger %A A. Sanpera %A J. Zakrzewski %X 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. %B Phys. Rev. A %I American Physical Society %V 83 %P 013605 %8 Jan %U http://link.aps.org/doi/10.1103/PhysRevA.83.013605 %R 10.1103/PhysRevA.83.013605 %0 Journal Article %J Journal of Low Temperature Physics %D 2011 %T Spin Effects in Bose-Glass Phases %A S. Paganelli %A M. Lacki %A V. Ahufinger %A J. Zakrzewski %A A. Sanpera %K Bose glass %K Spin-1 Bose Hubbard model %K Ultracold atoms %X 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' 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. %B Journal of Low Temperature Physics %I {SPRINGER/PLENUM PUBLISHERS} %C {233 SPRING ST, NEW YORK, NY 10013 USA} %V 165 %P 227-238 %8 DEC %R 10.1007/s10909-011-0392-7 %0 Journal Article %J Phys. Rev. A %D 2008 %T Double-barrier potentials for matter-wave gap solitons %A V. Ahufinger %A B. A. Malomed %A G. Birkl %A R. Corbalán %A A. Sanpera %X 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. %B Phys. Rev. A %I American Physical Society %V 78 %P 013608 %8 Jul %U http://link.aps.org/doi/10.1103/PhysRevA.78.013608 %R 10.1103/PhysRevA.78.013608 %0 Journal Article %J New Journal of Physics %D 2007 %T Quantum switches and quantum memories for matter-wave lattice solitons %A V. Ahufinger %A A Mebrahtu %A R. Corbalán %A A. Sanpera %X We study the possibility of implementing a quantum switch and a quantum memory using matter-wave lattice solitons and making them interact with 'effective' potentials (barrier/well) corresponding to defects of the optical lattice. In the case of interaction with an 'effective' 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 'effective' 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. %B New Journal of Physics %V 9 %P 4 %U http://stacks.iop.org/1367-2630/9/i=1/a=004 %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 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. Lett. %D 2005 %T Lattice Solitons in Quasicondensates %A V. Ahufinger %A A. Sanpera %X 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. %B Phys. Rev. Lett. %I American Physical Society %V 94 %P 130403 %8 Apr %U http://link.aps.org/doi/10.1103/PhysRevLett.94.130403 %R 10.1103/PhysRevLett.94.130403 %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