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arXiv:1009.2475 · Physical Review Letters

Observation of the Presuperfluid Regime in a Two-Dimensional Bose Gas

Shih-Kuang Tung, Giacomo Lamporesi, Daniel Lobser, Lin Xia, Eric Cornell

Published Dec 3, 2010• 120 citations
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Abstract

In complementary images of coordinate-space and momentum-space density in a trapped 2D Bose gas, we observe the emergence of presuperfluid behavior. As phase-space density $\ensuremath{\rho}$ increases toward degenerate values, we observe a gradual divergence of the compressibility $\ensuremath{\kappa}$ from the value predicted by a bare-atom model, ${\ensuremath{\kappa}}_{\mathrm{ba}}$. $\ensuremath{\kappa}/{\ensuremath{\kappa}}_{\mathrm{ba}}$ grows to 1.7 before $\ensuremath{\rho}$ reaches the value for which we observe the sudden emergence of a spike at $p=0$ in momentum space. Momentum-space images are acquired by means of a 2D focusing technique. Our data represent the first observation of non-mean-field physics in the presuperfluid but degenerate 2D Bose gas.

DOI
10.1103/physrevlett.105.230408

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In complementary images of coordinate-space and momentum-space density in a trapped 2D Bose gas, we observe the emergence of presuperfluid behavior. As phase-space density \ensuremathρ\ensuremath{\rho}\ensuremathρ increases toward degenerate values, we observe a gradual divergence of the compressibility \ensuremathκ\ensuremath{\kappa}\ensuremathκ from the value predicted by a bare-atom model, \ensuremathκba{\ensuremath{\kappa}}_{\mathrm{ba}}\ensuremathκba​. \ensuremathκ/\ensuremathκba\ensuremath{\kappa}/{\ensuremath{\kappa}}_{\mathrm{ba}}\ensuremathκ/\ensuremathκba​ grows to 1.7 before \ensuremathρ\ensuremath{\rho}\ensuremathρ reaches the value for which we observe the sudden emergence of a spike at p=0p=0p=0 in momentum space. Momentum-space images are acquired by means of a 2D focusing technique. Our data represent the first observation of non-mean-field physics in the presuperfluid but degenerate 2D Bose gas.
A fluctuating regime associated with the Berenzinskii-Kosterlitz-Thouless (BKT) transition is studied in a two-dimensional system of near-degenerate bosons (87Rb atoms). Two imaging procedures, the in-situ imaging method and the focusing-imaging method, are implemented to image the coordinate-space and momentum-space density distributions. The scaled compressibility is extracted from the coordinate-space density distributions obtained from in-situ images. Comparing the measured compressibility to the prediction from our semiclassical mean-field model, an onset of a regime which is beyond the mean-field prediction is identified and first resolved at phase-space density nλ2 ≳ 3. Information about the coherence of the system is extracted from the momentum-space distributions obtained from the focusing images. The spatial extent of the coherence at a size of the high density region in the system only appears at a distinguishably higher phase-space density of nλ2 ≈8. Therefore, a very interesting regime that is beyond mean-field prediction, but not yet a condensate, is identified. This regime, which does not exist in three dimensions, is a product of the enhanced interactions associated with reduced dimensionality.
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 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.
The physics in two-dimensional (2D) systems is very different from what we observe in three-dimensional (3D) systems. Thermal fluctuations in 2D systems are enhanced, and they prevent the conventional Bose-Einstein condensation (BEC) at non-zero temperatures by destroying the long-range order. However, a phase transition to a superfluid phase is still expected to occur in a 2D system along with an emergence of a quasi-long-range order, explained by the Berezinskii-Kosterlitz-Thouless (BKT) mechanism. Within the BKT mechanism, a universal jump of the superfluid density in a 2D Bosonic system was theoretically predicted by Nelson and Kosterlitz, and was first observed in 2D \textsuperscript{4}He films by Bishop and Reppy. Recent experiments in trapped ultracold 2D Bose gas systems have shown signatures of the BKT transition, and its superfluidity. However, the universal jump in the superfluid density was not observed in these systems. Here we report the first observation of the universal jump in the superfluid density using an optically trapped ultracold 2D Bose gas. The measured superfluid phase space density at the BKT transition agrees well with the predicted value within our measurement uncertainty. Additionally, we measure the phase fluctuations in our density profiles to show that the BKT transition occurs first, followed by the BEC transition.
We investigate the superfluid behavior of a two-dimensional (2D) Bose gas of 87Rb^{87}\mathrm{Rb}87Rb atoms using classical field dynamics. In the experiment by R. Desbuquois et al. [Nat. Phys. 8, 645 (2012)], a 2D quasicondensate in a trap is stirred with a blue-detuned laser beam along a circular path around the trap center. Here, we study this experiment from a theoretical perspective. The heating induced by stirring increases rapidly above a velocity vc{v}_{c}vc​, which we define as the critical velocity. We identify the superfluid, the crossover, and the thermal regime by a finite, a sharply decreasing, and a vanishing critical velocity, respectively. We demonstrate that the onset of heating occurs due to the creation of vortex-antivortex pairs. A direct comparison of our numerical results to the experimental ones shows a good agreement, if a systematic shift of the critical phase-space density is included. We relate this shift to the absence of thermal equilibrium between the condensate and the thermal wings, which were used in the experiment to extract the temperature. We expand on this observation by studying the full relaxation dynamics between the condensate and the thermal cloud.