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arXiv:cond-mat/0701616 · Physical Review Letters

Transition from a Two-Dimensional Superfluid to a One-Dimensional Mott Insulator

Sara Bergkvist, Anders Rosengren, Robert Saers, Emil Lundh, Magnus Rehn, Anders Kastberg

Published Sep 12, 2007• 6 citations
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Abstract

A two-dimensional system of atoms in an anisotropic optical lattice is studied theoretically. If the system is finite in one direction, it is shown to exhibit a transition between a two-dimensional superfluid and a one-dimensional Mott insulating chain of superfluid tubes. Monte Carlo simulations are consistent with the expectation that the phase transition is of Kosterlitz-Thouless type. The effect of the transition on experimental time-of-flight images is discussed.

DOI
10.1103/physrevlett.99.110401

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A two-dimensional system of atoms in an anisotropic optical lattice is studied theoretically. If the system is finite in one direction, it is shown to exhibit a transition between a two-dimensional superfluid and a one-dimensional Mott insulating chain of superfluid tubes. Monte Carlo simulations are consistent with the expectation that the phase transition is of Kosterlitz-Thouless type. The effect of the transition on experimental time-of-flight images is discussed.
We investigate the critical behaviors of correlation length and critical exponents for strongly interacting bosons in a two-dimensional optical lattice via quantum Monte Carlo simulations. By comparing the full numerical results to those given by the effective theory, we quantitatively determine the critical regime where the universal scaling behaviors apply at a finite temperature, for both classical Berezinskii-Kosterlitz-Thouless transition and quantum phase transition from superfluid to Mott insulator. Our results represent the critical regime that should be observed in present experimental conditions.
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The Mott insulator and superfluid phase transition is one of the most prominent phenomena in ultracold atoms. We report the observation of a novel 2D quantum phase transition between the Mott insulator and π superfluid in a shaking optical lattice. In the deep optical lattice regime, the lowest S band can be tuned to Mott phase, while the higher px,y bands are itinerant for having larger bandwidth. Through a shaking technique coupling the s-orbital to px,y -orbital states, we experimentally observe the transition between the states of the S and px,y bands, leading to a quantum phase transition from two-dimensional s-orbital Mott phase to the px,y -orbital superfluid which condensed at (π, π) momentum. Using the band-mapping method, we also observe the changes of atomic population in different energy bands during the transition, and the experimental results are well consistent with theoretical expectations.
We present numerical simulations on a lattice model of bosons in two dimensions using a path integral quantum Monte Carlo algorithm. At finite temperature we observe the Kosterlitz-Thouless transition and by a finite-size analysis determine the transition temperature. In the limit of zero temperature we find two distinct phases: at a special commensurate density (number of bosons integer multiple of the number of sites), the system is superfluid for small values of the interaction, but the superfluidity vanishes at a critical value of the interaction and the system becomes a Mott insulator. For an incommensurate density, the system remains superfluid at all values of the repulsive interaction between bosons. The superfluid density, however, vanishes as a commensurate density is approached for sufficiently large interaction. We estimate the critical exponents for these transitions.
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.
Abstract We study the superfluid to Mott‐insulator transition of bosons in an optical anisotropic lattice by employing the Bose‐Hubbard model living on a two‐dimensional lattice with anisotropy parameter κ. The compressible superfluid state and incompressible Mott‐insulator (MI) lobes are efficiently described analytically, using the quantum U(1) rotor approach. The ground state phase diagram showing the evolution of the MI lobes is quantified for arbitrary values of κ, corresponding to various kind of lattices: from square, through rectangular to almost one‐dimensional.