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arXiv:1112.0985 · Physical Review A

Effect of disorder close to the superfluid transition in a two-dimensional Bose gas

Baptiste Allard, Thomas Plisson, Markus Holzmann, Guillaume Salomon, Alain Aspect, Philippe Bouyer, Thomas Bourdel

Published Mar 2, 2012• 48 citations
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Abstract

We experimentally study the effect of disorder on trapped quasi-two-dimensional (2D) ${}^{87}$Rb clouds in the vicinity of the Berezinskii-Kosterlitz-Thouless (BKT) phase transition. The disorder correlation length is of the order of the Bose gas characteristic length scales (thermal de Broglie wavelength, healing length) and disorder thus modifies the physics at a microscopic level. We analyze the coherence properties of the cloud through measurements of the momentum distributions for two disorder strengths as a function of its degeneracy. For moderate disorder, the emergence of coherence remains steep but is shifted to a lower entropy. In contrast, for strong disorder, the growth of coherence is hindered. Our study is an experimental realization of the dirty boson problem in a well controlled atomic system suitable for quantitative analysis.

DOI
10.1103/physreva.85.033602

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We experimentally study the effect of disorder on trapped quasi-two-dimensional (2D) 87{}^{87}87Rb clouds in the vicinity of the Berezinskii-Kosterlitz-Thouless (BKT) phase transition. The disorder correlation length is of the order of the Bose gas characteristic length scales (thermal de Broglie wavelength, healing length) and disorder thus modifies the physics at a microscopic level. We analyze the coherence properties of the cloud through measurements of the momentum distributions for two disorder strengths as a function of its degeneracy. For moderate disorder, the emergence of coherence remains steep but is shifted to a lower entropy. In contrast, for strong disorder, the growth of coherence is hindered. Our study is an experimental realization of the dirty boson problem in a well controlled atomic system suitable for quantitative analysis.
We measure the momentum distribution of a two-dimensional trapped Bose gas and observe the increase of the range of coherence around the Berezinskii-Kosterlitz-Thouless (BKT) transition. We quantitatively compare our observed profiles to both a Hartree-Fock mean-field theory and quantum Monte Carlo simulations. In the normal phase, the momentum distribution is observed to sharpen well before the phase transition. This behavior is partially captured in a mean-field approach, in contrast to the physics of the BKT transition.
We present experimental results on a Bose gas in a quasi-2D geometry near the Berezinskii, Kosterlitz, and Thouless (BKT) transition temperature. By measuring the density profile after time of flight and the coherence length, we identify different states of the gas. We observe that the gas develops a bimodal distribution without long range order. In this regime, the gas presents a longer coherence length than the thermal cloud; it is quasicondensed but is not superfluid. Experimental evidence indicates that we also observe the superfluid transition (BKT transition). For a sufficiently long time of flight, we observe a trimodal distribution when the gas has developed a superfluid component.
We analyze the results of a recent experiment with bosonic rubidium atoms harmonically confined in a quasi-two-dimensional (2D) geometry. In this experiment a well-defined critical point was identified, which separates the high-temperature normal state characterized by a single component density distribution, and the low-temperature state characterized by a bimodal density distribution and the emergence of high-contrast interference between independent 2D clouds. We first show that this transition cannot be explained in terms of conventional Bose–Einstein condensation of the trapped ideal Bose gas. Using the local density approximation (LDA), we then combine the mean-field (MF) Hartree–Fock theory with the prediction for the Berezinskii–Kosterlitz–Thouless (BKT) transition in an infinite uniform system. If the gas is treated as a strictly 2D system, the MF predictions for the spatial density profiles significantly deviate from those of a recent quantum Monte Carlo (QMC) analysis. However, when the residual thermal excitation of the strongly confined degree of freedom is taken into account, excellent agreement is reached between the MF and the QMC approaches. For the interaction strength corresponding to the experiment, we predict a strong correction to the critical atom number with respect to the ideal gas theory (factor ∼2). Quantitative agreement between theory and experiment is reached concerning the critical atom number if the predicted density profiles are used for temperature calibration.
Long-range and anisotropic dipolar interactions induce complex order in quantum systems, particularly interesting in 2D where superfluidity emerges via the Berezinskii-Kosterlitz-Thouless (BKT) mechanism. We observe a superfluid phase with algebraically decaying correlation in a quasi-2D dipolar Bose gas of erbium atoms and further identify the superfluid phase transition by monitoring extended coherence. We also measure equations of state with tunable dipolar interactions. Our findings show a transition point shift due to dipole orientation, aligning with BKT transition with effective short-range interaction. However, we observe that in-plane tilted dipoles show nonlocal effects in the superfluid regime, preventing the effective short-range interaction from revealing universal behavior near the BKT critical point. We also measure anisotropic atom number fluctuations in the superfluid regime, highlighting its dipolar nature. Our results provide a foundation for understanding dipolar bosons in 2D and pave the way for investigating complex orders in dipolar superfluids.
We study the phase diagram of two-dimensional, interacting bosons in the presence of a correlated disorder in continuous space, by using large-scale quantum Monte Carlo simulations at finite temperature. We show that the superfluid transition is strongly protected against disorder. It remains of the Berezinskii-Kosterlitz-Thouless type up to disorder strengths comparable to the chemical potential. Moreover, we study the transport properties in the strong disorder regime where a zero-temperature Bose-glass phase is expected. We show that the conductance exhibits a thermally activated behavior vanishing only at zero temperature. Our results point towards the existence of a Bose bad-metal phase as a precursor of the Bose-glass phase.
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.