Feb 2012, Volume 7 Issue 1

Cover illustration

  • The robust quantum coherence and high controllability of Bose condensed atoms have led to many exciting advances in the field of quantum interferometry. Due to the atom-atom collisions, the systems of Bose condensed atoms are intrinsic nonlinear systems. In general, inter-particle interactions can be used to generate quantum entanglement and quantum entanglement can be utilized to enhance measurement precision. Therefore, it is important to control and exploit the nonlinear d [Detail] ...

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    Chaohong Lee, Peter D. Drummond, Masahito Ueda
    Andrey R. Kolovsky

    Quantum dynamics of a charged particle in a two-dimensional (2D) lattice subject to magnetic and electric fields is a rather complicated interplay between cyclotron oscillations (the case of vanishing electric field) and Bloch oscillations (zero magnetic field), details of which has not yet been completely understood. In the present work we suggest to study this problem by using cold atoms in optical lattices. We introduce a one-dimensional (1D) model which can be easily realized in laboratory experiments with quasi-1D optical lattices and show that this model captures many features of the cyclotron-Bloch dynamics of the quantum particle in 2D square lattices.

    Xi-Wen Guan

    Using solutions of the discrete Bethe ansatz equations, we study in detail the quantum impurity problem of a spin-down fermion immersed into a fully ploarized spin-up Fermi sea with weak attraction. We prove that this impurity fermion in the one-dimensional (1D) fermionic medium behaves like a polaron for weak attraction. However, as the attraction grows, the spin-down fermion binds with one spin-up fermion from the fully-polarized medium to form a tightly bound molecule. Thus it is seen that the system undergos a crossover from a mean field polaron-like nature into a mixture of excess fermions and a bosonic molecule as the attraction changes from weak attraction into strong attraction. This polaron–molecule crossover is universal in 1D many-body systems of interacting fermions. In a thermodynamic limit, we further study the relationship between the Fredholm equations for the 1D spin-1/2 Fermi gas with weakly repulsive and attractive delta-function interactions.

    Qiong-Yi He, Margaret D. Reid, Bogdan Opanchuk, Rodney Polkinghorne, Laura E. C. Rosales-Zárate, Peter D. Drummond

    We review recent developments in the theory of quantum dynamics in ultracold atomic physics, including exact techniques and methods based on phase-space mappings that are applicable when the complexity becomes exponentially large. Phase-space representations include the truncated Wigner, positive-P and general Gaussian operator representations which can treat both bosons and fermions. These phase-space methods include both traditional approaches using a phase-space of classical dimension, and more recent methods that use a non-classical phase-space of increased dimensionality. Examples used include quantum Einstein–Podolsky–Rosen (EPR) entanglement of a four-mode BEC, time-reversal tests of dephasing in single-mode traps, BEC quantum collisions with up to 106 modes and 105 interacting particles, quantum interferometry in a multi-mode trap with nonlinear absorption, and the theory of quantum entropy in phase-space. We also treat the approach of variational optimization of the sampling error, giving an elementary example of a nonlinear oscillator.

    Dan-wei Zhang (张丹伟), Zi-dan Wang (汪子丹), Shi-liang Zhu (朱诗亮)

    Quantum simulation is a powerful tool to study a variety of problems in physics, ranging from high-energy physics to condensed-matter physics. In this article, we review the recent theoretical and experimental progress in quantum simulation of Dirac equation with tunable parameters by using ultracold neutral atoms trapped in optical lattices or subject to light-induced synthetic gauge fields. The effective theories for the quasiparticles become relativistic under certain conditions in these systems, making them ideal platforms for studying the exotic relativistic effects. We focus on the realization of one, two, and three dimensional Dirac equations as well as the detection of some relativistic effects, including particularly the well-known Zitterbewegung effect and Klein tunneling. The realization of quantum anomalous Hall effects is also briefly discussed.

    Alexander Yu. Cherny, Jean-Sébastien Caux, Joachim Brand

    The one-dimensional Bose gas is an unusual superfluid. In contrast to higher spatial dimensions, the existence of non-classical rotational inertia is not directly linked to the dissipationless motion of infinitesimal impurities. Recently, experimental tests with ultracold atoms have begun and quantitative predictions for the drag force experienced by moving obstacles have become available. This topical review discusses the drag force obtained from linear response theory in relation to Landau’s criterion of superfluidity. Based upon improved analytical and numerical understanding of the dynamical structure factor, results for different obstacle potentials are obtained, including single impurities, optical lattices and random potentials generated from speckle patterns. The dynamical breakdown of superfluidity in random potentials is discussed in relation to Anderson localization and the predicted superfluid–insulator transition in these systems.

    Margaret D. Reid, Qiong-Yi He, Peter D. Drummond

    Entanglement, the Einstein–Podolsky–Rosen (EPR) paradox and Bell’s failure of local-hiddenvariable (LHV) theories are three historically famous forms of “quantum nonlocality”. We give experimental criteria for these three forms of nonlocality in multi-particle systems, with the aim of better understanding the transition from microscopic to macroscopic nonlocality. We examine the nonlocality of N separated spin J systems. First, we obtain multipartite Bell inequalities that address the correlation between spin values measured at each site, and then we review spin squeezing inequalities that address the degree of reduction in the variance of collective spins. The latter have been particularly useful as a tool for investigating entanglement in Bose–Einstein condensates (BEC). We present solutions for two topical quantum states: multi-qubit Greenberger–Horne–Zeilinger (GHZ) states, and the ground state of a two-well BEC.

    Alice Sinatra, Jean-Christophe Dornstetter, Yvan Castin

    We consider dynamically generated spin squeezing in interacting bimodal condensates. We show that particle losses and non-zero temperature effects in a multimode theory completely change the scaling of the best squeezing for large atom numbers. We present the new scalings and we give approximate analytical expressions for the squeezing in the thermodynamic limit. Besides reviewing our recent theoretical results, we give here a simple physical picture of how decoherence acts to limit the squeezing. We show in particular that under certain conditions the decoherence due to losses and non-zero temperature acts as a simple dephasing.

    Hui Hu

    Recent breakthroughs in the creation of ultracold atomic gases in the laboratory have ushered in major changes in physical science. Many novel experiments are now possible, with an unprecedented control of interaction, geometry and purity. Quantum many-body theory is facing severe challenges in quantitatively understanding new experimental results. Here, we review some recently developed theoretical techniques that provide successful predictions for density response of a strongly correlated atomic Fermi gas. These include the strong-coupling random-phase approximation theory, hightemperature quantum virial expansion, and asymptotically exact Tan relations applicable at large momentum.

    Chaohong Lee, Jiahao Huang, Haiming Deng, Hui Dai, Jun Xu

    In quantum interferometry, it is vital to control and utilize nonlinear interactions for the achievement of high-precision measurements. Due to their long coherence time and high controllability, ultracold atoms including Bose condensed atoms have been widely used for quantum interferometry. Here, we review recent progress in theoretical studies of quantum interferometry with Bose condensed atoms. In particular, we focus on nonlinear phenomena induced by atom–atom interactions, and how to control and utilize these nonlinear phenomena. With a mean-field description, due to atom–atom interactions, matter-wave solitons appear in the interference patterns, and macroscopic quantum self-trapping exists in Bose–Josephson junctions. With a many-body description, atom–atom interactions can generate non-classical entanglement, which can be utilized to achieve high-precision measurements beyond the standard quantum limit.

    M. A. Garcia-March, D. R. Dounas-Frazer, Lincoln D. Carr

    We present a thorough description of the physical regimes for ultracold bosons in double wells, with special attention paid to macroscopic superpositions (MSs). We use a generalization of the Lipkin–Meshkov–Glick Hamiltonian of up to eight single particle modes to study these MSs, solving the Hamiltonian with a combination of numerical exact diagonalization and high-order perturbation theory. The MS is between left and right potential wells; the extreme case with all atoms simultaneously located in both wells and in only two modes is the famous NOON state, but our approach encompasses much more general MSs. Use of more single particle modes brings dimensionality into the problem, allows us to set hard limits on the use of the original two-mode LMG model commonly treated in the literature, and also introduces a mixed Josephson–Fock regime. Higher modes introduce angular degrees of freedom and MS states with different angular properties.