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arXiv:cond-mat/0511437 · Journal of Physics B Atomic Molecular and Optical Physics

Finite-temperature renormalization group analysis of interaction effects in 2D lattices of Bose–Einstein condensates

Augusto Smerzi, Pasquale Sodano, Andrea Trombettoni

Published Mar 24, 2004• 7 citations
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Abstract

By using a renormalization group analysis, we study the effect of interparticle interactions on the critical temperature at which the Berezinskii-Kosterlitz-Thouless (BKT) transition occurs for Bose-Einstein condensates loaded at finite temperature in a 2D optical lattice. We find that the critical temperature decreases as the interaction energy decreases; when U/J=36/πone has a vanishing critical temperature, signaling the possibility of a quantum phase transition of BKT type.

DOI
10.1088/0953-4075/37/7/071

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By using a renormalization group analysis, we study the effect of interparticle interactions on the critical temperature at which the Berezinskii-Kosterlitz-Thouless (BKT) transition occurs for Bose-Einstein condensates loaded at finite temperature in a 2D optical lattice. We find that the critical temperature decreases as the interaction energy decreases; when U/J=36/πone has a vanishing critical temperature, signaling the possibility of a quantum phase transition of BKT type.
We investigate the possibility that Bose-Einstein condensates (BECs), loaded on a 2D optical lattice, undergo- at finite temperature- a Berezinskii-Kosterlitz-Thouless (BKT) transition. We show that- in an experimentally attainable range of parameters- a planar lattice of BECs is described by the XY model at finite temperature. We demonstrate that the interference pattern of the expanding condensates provides the experimental signature of the BKT transition by showing that, near the critical temperature, the ⃗k = 0 component of the momentum distribution and the central peak of the atomic density profile sharply decrease. The finite-temperature transition for a 3D optical lattice is also discussed, and the analogies with superconducting Josephson junction networks are stressed through the text. 1 I.
We discuss the finite-temperature properties of Bose-Einstein condensates loaded on a 2D optical lattice. In an experimentally attainable range of parameters the system is described by the XY model, which undergoes a Berezinskii-Kosterlitz-Thouless (BKT) transition driven by the vortex pair unbinding. The interference pattern of the expanding condensates provides the experimental signature of the BKT transition: near the critical temperature, the k=0 component of the momentum distribution sharply decreases.
We investigate the possibility that Bose–Einstein condensates, loaded on a 2D optical lattice, undergo—at finite temperature—a Berezinskii–Kosterlitz–Thouless transition. We show that—in an experimentally attainable range of parameters—a planar lattice of Bose–Einstein condensates is described by the XY model at finite temperature. We demonstrate that the interference pattern of the expanding condensates provides the experimental signature of the Berezinskii–Kosterlitz–Thouless transition by showing that, near the critical temperature, the component of the momentum distribution and the central peak of the atomic density profile sharply decrease. The finite-temperature transition for a 3D optical lattice is also discussed in this paper, and analogies with superconducting Josephson junction networks are stressed throughout the text.
We prepare and study strongly interacting two-dimensional Bose gases in the superfluid, the classical Berezinskii-Kosterlitz-Thouless (BKT) transition, and the vacuum-to-superfluid quantum critical regimes. A wide range of the two-body interaction strength 0.05 < g < 3 is covered by tuning the scattering length and by loading the sample into an optical lattice. Based on the equations of state measurements, we extract the coupling constants as well as critical thermodynamic quantities in different regimes. In the superfluid and the BKT transition regimes, the extracted coupling constants show significant down-shifts from the mean-field and perturbation calculations when g approaches or exceeds one. In the BKT and the quantum critical regimes, all measured thermodynamic quantities show logarithmic dependence on the interaction strength, a tendency confirmed by the extended classical-field and renormalization calculations.
Recent experiments on ultracold Bose gases in two dimensions have provided evidence for the existence of the Berezinskii-Kosterlitz-Thouless (BKT) phase via analysis of the interference between two independent systems. In this work we study the two-dimensional quantum degenerate Bose gas at finite temperature using the projected Gross-Pitaevskii equation classical field method. Although this describes the highly occupied modes of the gas below a momentum cutoff, we have developed a method to incorporate the higher momentum states in our model. We concentrate on finite-sized homogeneous systems in order to simplify the analysis of the vortex pairing. We determine the dependence of the condensate fraction on temperature and compare this to the calculated superfluid fraction. By measuring the first order correlation function we determine the boundary of the Bose-Einstein condensate and BKT phases, and find it is consistent with the superfluid fraction decreasing to zero. We reveal the characteristic unbinding of vortex pairs above the BKT transition via a coarse-graining procedure. Finally, we model the procedure used in experiments to infer system correlations [Hadzibabic et al., Nature 441, 1118 (2006)], and quantify its level of agreement with directly calculated in situ correlation functions.
Abstract We study the behavior of interacting ultracold bosons in a two-dimensional optical lattice described by the Bose–Hubbard (BH) model. We apply the quantum rotor approach to reduce the BH model to a (semiclassical) effective Hamiltonian in which the phases of local order parameters play the role of dynamical variables. This leads to the effective quantum XY model, which is used to calculate the Berezinskii–Kosterlitz–Thouless transition temperature T BKT as a function of model parameters. We find that T BKT is monotonically dependent on the kinetic energy of atoms and the value of the chemical potential.