Detecting the superfluid critical momentum of Bose gases in optical lattices through dipole oscillations

Abstract

We study stability of superflow of Bose gases in optical lattices by analyzing the Bose-Hubbard model within the Gutzwiller mean-field approximation. We calculate the excitation spectra of the homogeneous Bose-Hubbard model at unit filling to determine the critical momenta for the Landau and dynamical instabilities. These two critical momenta are shown to approach each other when the on-site interaction increases towards the Mott transition point. In order to make a direct connection with realistic experiments, we next take into account a parabolic trapping potential and compute the real-time dynamics of dipole oscillations induced by suddenly displacing the trap center. We consider the following two cases: standard softcore bosons, whose interparticle interactions include the on-site one only, and hardcore bosons with long-range dipole-dipole interactions. For both cases, we show that the dipole oscillation is significantly damped when the maximum local momentum exceeds a certain threshold, which quantitatively agrees with the critical momentum for the dynamical instability in the homogeneous system. In the case of dipolar hardcore bosons, the dynamical instability of dipole oscillations leads to the formation of checkerboard density waves in the superfluid phase near the boundary to the supersolid phase.

Dynamic phase diagram for the quantum phase model

“…An analytic form for the modulational instability critical line is derived from the study of the linear dynamics of the perturbations over the current-carrying stationary states. The lines for one-, two-, and three-dimensional lattices are in good agreement with the results obtained for the Bose-Hubbard model from the integration of the mean-field dynamics [5,6] and the numerical study of the excitation spectra [10]. Also, we are able to provide analytical results for the phase gradient attaining the maximal superfluid current, and for the energetic instability threshold.…”

“…Note the qualitative agreement of the curves in this figure with the analogous results obtained numerically in Refs. [5,6,10]. As discussed in Sec.…”

“…As we mention, this result does not hold true in general. Studies based on the Gross-Pitaevskii equation [2], discrete nonlinear Schrödinger equation [16], and the Gutzwiller equations for the Bose-Hubbard model [10,18] show that there exists a finite range of p in which the stationary states are dynamically stable but energetically unstable. However, it can be shown [18] that this interval shrinks with increasing interaction and average site occupancy, and it is hence expected to be negligible in the regime where the QPM applies.…”

“…These analytic results are qualitatively similar to those obtained numerically in Refs. [5,6,10] for the BoseHubbard model. We note that for vanishing p the threshold for dynamical instability collapses to the critical point for the transition to the insulating state (2) 0 = (1) 0 , which is also in agreement with the mentioned references.…”

Localized Higgs modes of superfluid Bose gases in optical lattices: A Gutzwiller mean-field study

“…While the Gutzwiller approach is a simple mean-field approximation, it has been extensively applied to describing various properties of the Bose-Hubbard model, such as quantum phase transitions [49][50][51], collective modes [51][52][53][54], the superfluid critical momentum [54,55], and nonequilibrium dynamics [19,[54][55][56][57][58]. In order to describe collective modes of the system, we separate f i,n (t) into its static part and small fluctuations,…”