Observation of the Berezinskii-Kosterlitz-Thouless Phase Transition in an Ultracold Fermi Gas

Abstract

We experimentally investigate the first-order correlation function of a trapped Fermi gas in the two-dimensional BEC-BCS crossover. We observe a transition to a low-temperature superfluid phase with algebraically decaying correlations. We show that the spatial coherence of the entire trapped system can be characterized by a single temperature-dependent exponent. We find the exponent at the transition to be constant over a wide range of interaction strengths across the crossover. This suggests that the phase transitions in both the bosonic regime and the strongly interacting crossover regime are of Berezinskii-Kosterlitz-Thouless type and lie within the same universality class. On the bosonic side of the crossover, our data are well-described by the quantum Monte Carlo calculations for a Bose gas. In contrast, in the strongly interacting regime, we observe a superfluid phase which is significantly influenced by the fermionic nature of the constituent particles.Long-range coherence is the hallmark of superfluidity and Bose-Einstein condensation [1,2]. The character of spatial coherence in a system and the properties of the corresponding phase transitions are fundamentally influenced by dimensionality. The two-dimensional case is particularly intriguing as for a homogeneous system, true long-range order cannot persist at any finite temperature due to the dominant role of phase fluctuations with large wavelengths [3][4][5]. Although this prevents Bose-Einstein condensation in 2D, a transition to a superfluid phase with quasi-long-range order can still occur, as pointed out by Berezinskii, Kosterlitz, and Thouless (BKT) [6][7][8]. A key prediction of this theory is the scale-invariant behavior of the first-order correlation function g 1 (r), which, in the low-temperature phase, decays algebraically according to g 1 (r) ∝ r −η for large separations r. Importantly, the BKT theory for homogeneous systems predicts a universal value of η c = 1/4 at the critical temperature, accompanied by a universal jump of the superfluid density [9].Several key signatures of BKT physics have been experimentally observed in a variety of systems such as exciton-polariton condensates [10], layered magnets [11,12], liquid 4 He films [13], and trapped Bose gases [14][15][16][17][18][19][20]. Particularly in the context of superfluidity, the universal jump in the superfluid density was measured in thin films of liquid 4 He [13]. More recently, in the pioneering interference experiment with a weakly interacting Bose gas [14], the emergence of quasi-long-range order and the proliferation of vortices were shown.There are still important aspects of superfluidity in two-dimensional systems that remain to be understood, which we aim to elucidate in this work with ultracold atoms. One question is whether the BKT phenomenology can also be extended to systems with nonuniform density. Indeed, if the microscopic symmetries are the same, the general physical picture involving phase fluctuations should be valid also for inhomogeneous systems. However, it ...

Two-dimensional spin-imbalanced Fermi gases at nonzero temperature: Phase separation of a noncondensate

“…Proving the existence or non-existence of true phase coherence would lead to a significant advance in the understanding of the physics of 2D Fermi gases. As in previous work [15,17,18] true superfluidity in 2D has not been established here or in experiments. This will require future experimental probes related to coherence features, including interference measurements, or detection of the presence of collective modes in Bragg scattering.…”

“…The evidence from experiments [17,18] on 2D spinbalanced Fermi gases suggests that the bosonic degrees of freedom (accessed by rapid magnetic field sweeps) exhibit strong |q| → 0 peaks in their momentum distribution, represented by a trap-average, denotedn B (q), of n B (q) = b q 2 /2M B − µ pair appearing in Eq. (2).…”

“…1(a), shows that for moderate polarizations the range in radii over which one has pairing (and therefore quasi-condensation) is restricted. This makes it difficult to perform the analysis that addresses power laws vs exponential fitting functions in the Fourier transform ofn B (q), which was identified [18] with g 1 (r). For the unpolarized case, such an analysis [15] further substantiated the identification of T qc with the expression in Eq.…”

Fermions in Two Dimensions: Scattering and Many-Body Properties

“…A rich area of study subject to ongoing investigation is that of low dimensionality [16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38]. These dilute cold atomic gases have been trapped using anisotropic potentials, resulting in a quasi-2D pancake-shape gas cloud.…”

Finite-range corrections to the thermodynamics of the one-dimensional Bose gas

“…As recently shown for the 2D Bose gas [24], since finiterange corrections affect the behavior of quantum and thermal fluctuations, they have to be taken into account also in lower dimensional system, where fluctuations are strongly enhanced (Mermin-Wagner-Hohenberg theorem [25,26]). Improvements in cold-atom experimental techniques are providing a precision benchmark which makes possible to explore in great details beyond-mean-field effects in low-dimensional systems [5,6,27,28]. It was recently shown, both theoretically and experimentally, that quantum fluctuations provides a stabilization mechanism against collapse, as predicted by the mean-field theory, both in dipolar condensate and binary Bose mixture [29][30][31][32][33].…”