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arXiv:0711.1423 · Physical Review A

Superfluidity of an interacting trapped quasi-two-dimensional Bose gas

Tapio Simula, Matthew J. Davis, P. B. Blakie

Published Feb 19, 2008• 43 citations
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Abstract

We investigate the harmonically trapped interacting Bose gas in a quasi-two-dimensional geometry using the classical field method. The system exhibits quasi-long-range order and nonclassical rotational inertia at temperatures below the Berezinskii-Kosterlitz-Thouless crossover to the superfluid state. In particular, we compute the scissors-mode oscillation frequencies and find that the irrotational mode changes its frequency as the temperature is swept across the crossover thus providing microscopic evidence for the emergence of superfluidity.

DOI
10.1103/physreva.77.023618

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We investigate the harmonically trapped interacting Bose gas in a quasi-two-dimensional geometry using the classical field method. The system exhibits quasi-long-range order and nonclassical rotational inertia at temperatures below the Berezinskii-Kosterlitz-Thouless crossover to the superfluid state. In particular, we compute the scissors-mode oscillation frequencies and find that the irrotational mode changes its frequency as the temperature is swept across the crossover thus providing microscopic evidence for the emergence of superfluidity.
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We report direct evidence of superfluidity in a quasi two-dimensional Bose gas by observing its dynamical response to a collective excitation, the scissors mode. Relying on a novel local average analysis, we are able to probe inhomogeneous clouds and reveal their local dynamics. We identify in this way the superfluid and thermal phases inside the gas and locate the boundary at which the Berezinskii–Kosterlitz–Thouless crossover occurs. This new analysis also allows to evidence the coupling of the two fluids which induces at finite temperatures damping rates larger than the usual Landau damping.
We study the critical point for the emergence of coherence in a harmonically trapped two-dimensional Bose gas with tunable interactions. Over a wide range of interaction strengths we find excellent agreement with the classical-field predictions for the critical point of the Berezinskii-Kosterlitz-Thouless (BKT) superfluid transition. This allows us to quantitatively show, without any free parameters, that the interaction-driven BKT transition smoothly converges onto the purely quantum-statistical Bose-Einstein condensation transition in the limit of vanishing interactions.
We simulate a trapped quasi-two-dimensional Bose gas using a classical field method. To interpret our results we identify the uniform Berezinskii-Kosterlitz-Thouless (BKT) temperature TBKT{T}_{\text{BKT}}TBKT​ as where the system phase-space density satisfies a critical value. We observe that density fluctuations are suppressed in the system well above TBKT{T}_{\text{BKT}}TBKT​ when a quasicondensate forms as the first occurrence of degeneracy. At lower temperatures, but still above TBKT{T}_{\text{BKT}}TBKT​, we observe the development of appreciable coherence as a prominent finite-size effect, which manifests as bimodality in the momentum distribution of the system. At TBKT{T}_{\text{BKT}}TBKT​ algebraic decay of off-diagonal correlations occurs near the trap center with an exponent of 0.25, as expected for the uniform system. Our results characterize the low-temperature phase diagram for a trapped quasi-two-dimensional Bose gas and are consistent with observations made in recent experiments.
We study the quasi-two-dimensional Bose gas in harmonic traps at temperatures above the Kosterlitz-Thouless transition, where the gas is in the normal phase. We show that mean-field theory takes into account the dominant interaction effects for experimentally relevant trap geometries. Comparing with quantum Monte Carlo calculations, we quantify the onset of the fluctuation regime, where correlations beyond mean-field become important. Although the density profile depends on the microscopic parameters of the system, we show that the correlation density (the difference between the exact and the mean-field density) is accurately described by a universal expression, obtained from classical-field calculations of the homogeneous strictly two-dimensional gas. Deviations from universality, due to the finite value of the interaction or to the trap geometry, are shown to be small for current experiments. We further study coherence and pair correlations on a microscopic scale. Finite-size effects in the off-diagonal density matrix allow us to characterize the crossover from Kosterlitz-Thouless to Bose-Einstein behavior for small particle numbers. Bose-Einstein condensation occurs below a characteristic number of particles which rapidly diverges with vanishing interactions.