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arXiv:cond-mat/0408437 · Physical Review Letters

Mott-Insulator Phase of Coupled One-Dimensional Atomic Gases in a Two-Dimensional Optical Lattice

Dimitri M. Gangardt, P. Pedri, Luis Santos, Gora V. Shlyapnikov

Published Jan 31, 2006• 11 citations
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Abstract

We consider the 2D Mott-insulator state of a 2D array of coupled finite size 1D Bose gases. It is shown that the momentum distribution in the lattice plane is very sensitive to the interaction regime in the 1D tubes. In particular, we find that the disappearance of the interference pattern in time-of-flight experiments is a clear consequence of the strongly interacting Tonks-Girardeau regime along the tubes.

DOI
10.1103/physrevlett.96.040403

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We consider the 2D Mott-insulator state of a 2D array of coupled finite size 1D Bose gases. It is shown that the momentum distribution in the lattice plane is very sensitive to the interaction regime in the 1D tubes. In particular, we find that the disappearance of the interference pattern in time-of-flight experiments is a clear consequence of the strongly interacting Tonks-Girardeau regime along the tubes.
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 report the Bragg spectroscopy of interacting one-dimensional Bose gases loaded in an optical lattice across the superfluid to the Mott-insulator phase transition. Elementary excitations are created with a nonzero momentum and the response of the correlated 1D gases is in the linear regime. The complexity of the strongly correlated quantum phases is directly displayed in the spectra which exhibit novel features. This work paves the way for a precise characterization of the state of correlated gases in optical lattices.
The loading of a Bose-Einstein condensate into a deep two-dimensional optical lattice provides a unique way to study one-dimensional Bose gases: the strong radial confinement freezes any motion in two dimensions, and for deep enough lattices, the system can be seen as an array of independent I D tubers. For our experimental parameters, the ID gas is predicted to be in an intermediate regime between the Tonks-Girardeau and the Thomas-Fermi regimes. We performed experiments showing that some long range phase coherence is present in this regime. We investigated correlation properties of these gases by studying their collective oscillations. In addition, we investigated the ID Mott transition by adiabatically loading the 1D gases into a 1D optical lattice.
Synthetic spin-orbit coupling in ultracold atomic gases can be taken to extremes rarely found in solids. We study a two-dimensional Hubbard model of bosons in an optical lattice in the presence of spin-orbit coupling strong enough to drive direct transitions from Mott insulators to superfluids. Here we find phase-modulated superfluids with finite momentum that are generated entirely by spin-orbit coupling. We investigate the rich phase patterns of the superfluids, which may be directly probed using time-of-flight imaging of the spin-dependent momentum distribution.