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arXiv:cond-mat/0605419 · New Journal of Physics

Interacting Bose gases in quasi-one-dimensional optical lattices

Miguel A. Cazalilla, A F Ho, Thierry Giamarchi

Published Aug 30, 2006• 70 citations
arXivHTMLPDF

Abstract

We study a two-dimensional (2D) array of coupled 1D tubes of interacting bosons. Such systems can be produced by loading ultracold atoms in anisotropic optical lattices. We investigate the effects of coupling the tubes via hopping of the bosons (i.e. Josephson coupling). In the absence of a periodic potential along the tubes, or when such potential is incommensurate with the boson density, the system undergoes a transition from an array of incoherent Tomonaga–Luttinger liquids at high temperature to an anisotropic Bose–Einstein condensate (BEC), at low temperature. We determine the transition temperature and long wavelength excitations of the BEC. In addition to the usual gapless (Goldstone) mode found in standard superfluids, we also find a gapped mode associated with fluctuations of the amplitude of the order parameter. When a commensurate periodic potential is applied along the tubes, they can become 1D Mott insulators. Intertube hopping leads to a deconfinement quantum phase transition between the 1D Mott insulators and the anisotropic BEC. We also take into account the finite size of the gas tubes as realized in actual experiments. We map out the phase diagram of the quasi-1D lattice and compare our results with the existing experiments on such systems.

DOI
10.1088/1367-2630/8/8/158

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We study a two-dimensional (2D) array of coupled 1D tubes of interacting bosons. Such systems can be produced by loading ultracold atoms in anisotropic optical lattices. We investigate the effects of coupling the tubes via hopping of the bosons (i.e. Josephson coupling). In the absence of a periodic potential along the tubes, or when such potential is incommensurate with the boson density, the system undergoes a transition from an array of incoherent Tomonaga–Luttinger liquids at high temperature to an anisotropic Bose–Einstein condensate (BEC), at low temperature. We determine the transition temperature and long wavelength excitations of the BEC. In addition to the usual gapless (Goldstone) mode found in standard superfluids, we also find a gapped mode associated with fluctuations of the amplitude of the order parameter. When a commensurate periodic potential is applied along the tubes, they can become 1D Mott insulators. Intertube hopping leads to a deconfinement quantum phase transition between the 1D Mott insulators and the anisotropic BEC. We also take into account the finite size of the gas tubes as realized in actual experiments. We map out the phase diagram of the quasi-1D lattice and compare our results with the existing experiments on such systems.
We study the thermodynamic properties of a 2D array of coupled one-dimensional Bose gases. The system is realized with ultracold bosonic atoms loaded in the potential tubes of a two-dimensional optical lattice. For negligible coupling strength, each tube is an independent weakly interacting 1D Bose gas featuring Tomonaga Luttinger liquid behavior. By decreasing the lattice depth, we increase the coupling strength between the 1D gases and allow for the phase transition into a 3D condensate. We extract the phase diagram for such a system and compare our results with theoretical predictions. Because of the high effective mass across the periodic potential and the increased 1D interaction strength, the phase transition is shifted to large positive values of the chemical potential. Our results are prototypical to a variety of low-dimensional systems, where the coupling between the subsystems is realized in a higher spatial dimension such as coupled spin chains in magnetic insulators.
We investigate the behavior of an array of Bose-Einstein condensate tubes described by means of a Bose-Hubbard Hamiltonian. Using an anisotropic non-polynomial Schrodinger equation we link the macroscopic parameters in the Bose-Hubbard Hamiltonian to the ones that are tunable in experiments. Using a mean field approach we predict that increasing the optical lattice strength along the direction of the tubes, the condensate can experience a reentrant transition between a Mott insulating phase and the superfluid one.
We study ground-state phase diagrams and excitation spectra of Bose-Bose mixtures in an optical lattice by applying the Gutzwiller approximation to the two-component Bose-Hubbard model. A case of equal hoppings and equal intra-component interactions for both components is considered. Due to the existence of inter-component interaction, there appear several quantum phases, such as the superfluid, paired superfluid, and counterflow superfluid phases. We find that the transition from superfluid (SF) to Mott insulator (MI) with even filling factors can be of the first order for a wide range of the chemical potential. We calculate the excitation spectra as a useful probe to identify the quantum phases and the SF-to-MI transitions. In the excitation spectra of the SF phase, there are two gapless modes and a few gapful modes, which respectively correspond to phase and amplitude fluctuations of the order parameters. At the SF-to-MI transition point, we show that the energy gaps of certain amplitude modes reach zero for the second-order transition while they remain finite for the first-order one. Since the excitation spectrum can be measured by the Bragg scattering, we calculate the dynamical structure factor by using the linear response theory. We consider three types of density fluctuations, and show that the density fluctuations are coupled to different excitation branches in different quantum phases.
Quantum degenerate atomic gases offer a unique platform for the exploration of a wide variety of interacting many-body systems in a pristine environment, based on a set of powerful tools for the coherent control of the atoms' internal and external degrees of freedom. Here, we present experimental studies of strongly interacting bosonic mixtures in one-dimensional (1D) systems, in which the mobilities of the two species are independently controlled with a state-selective optical lattice. In a first experiment, we freeze out the tunneling of one species from a binary mixture, and study the formation of ``quantum emulsion'' states, where immobile atoms serve as a static, random disorder for a more mobile species. We investigate the 1D superfluid-to-insulator transition in the presence of this disorder, and make comparisons to the effects of quasi-disorder from an incommensurate optical lattice. We observe enhanced localization in the more random potential, highlighting the important role of correlations in disordered systems. Through a combined measurement of transport, localization, and excitation spectra, we are able to obtain strong evidence for observation of a disordered, insulating quantum phase, the 1D Bose glass. In a second experiment, we introduce a new experimental technique for the characterization of ultracold gases held in optical lattices. In analogy to neutron diffraction from solids, we use atomic de Broglie waves to non-destructively probe the spatial structure of 1D Mott insulators through elastic Bragg diffraction, and to probe inelastic band-structure excitations of more weakly interacting 1D Bose gases. Furthermore, we use the diffraction of matter waves to detect the formation of forced-antiferromagnetic ordering in a crystalline atomic spin mixture. Lastly, we study the dynamical response of matter waves to a periodically pulsed, incommensurate optical lattice, a situation that realizes a system of two coupled kicked quantum rotors. We observe that the coupling induces a suppression of energy growth at quantum resonances, and a localization-to-delocalization transition in momentum space for off-resonant driving. Our observations confirm a long-standing theoretical prediction for the two-rotor system, and illustrate how classical behavior can emerge from the evolution of a simple quantum system. | 193 pages
We study phase transitions of coupled two dimensional XY systems with spatial anisotropy and U(1)×Z2U(1) \times \mathbb{Z}_2U(1)×Z2​ symmetry, motivated by spinless bosonic atoms trapped in square optical lattice on the metastable first excited p−p-p−level orbitals with anisotropic hopping amplitudes. The phase transitions of the system are generally split into an Ising transition and an XY transition, but the sequence and the nature of the transitions depend on the ratio between the anisotropic couplings. In the isotropic limit the XY variables are expected to be disordered before the Ising variables when thermal or quantum fluctuations are turned on gradually. In the anisotropic limit with zero perpendicular hoppings, the finite temperature transition is a Kosterlitz-Thouless transition driven by proliferation of hybrid half vortices, and the zero temperature quantum phase transition is split into a bond order transition and a 3D XY transition, which can be driven by the condensation of either single vortices or half vortices. After the condensation of half vortices the resultant state is a Mott Insulator of paired bosons. A small perpendicular hopping JbJ_bJb​ leads to a 2D Ising transition at low temperature and a 2+1d quantum Ising transition with a small charging energy at zero temperature. Global phase diagrams for both classical and quantum phase transitions are drawn. The analytical results obtained in this work are expected to be checked both numerically and experimentally.