Superfluid density and critical velocity near the Berezinskii-Kosterlitz-Thouless transition in a two-dimensional strongly interacting Fermi gas

Abstract

We theoretically investigate superfluidity in a strongly interacting Fermi gas confined to two dimensions at finite temperature. Using a Gaussian pair fluctuation theory in the superfluid phase, we calculate the superfluid density and determine the critical temperature and chemical potential at the Berezinskii-Kosterlitz-Thouless transition. We propose that the transition can be unambiguously demonstrated in cold-atom experiments by stirring the superfluid Fermi gas using a red detuned laser beam, to identify the characteristic jump in the local Landau critical velocity at the superfluidnormal interface, as the laser beam moves across the cloud.PACS numbers: 03.75. Ss, 03.70.+k, 05.70.Fh, 03.65.Yz In two-dimensional (2D) many-body systems, topologically nontrivial vortex fluctuations, that are suppressed due to vortex/anti-vortex binding at low temperature, become amplified above a certain critical temperature, leading to the so-called Berezinskii-Kosterlitz-Thouless (BKT) transition [1][2][3]. The BKT transition has been of great importance in different branches of physics and has been observed in a range of settings [4][5][6][7]. In particular, ultracold atomic gases are an ideal candidate to understand the interaction-driven BKT physics [7], owing to the unprecedented controllability over interatomic interactions, dimensionality and species [8]. Over the past decade, the BKT transition in a 2D weakly interacting Bose gas has been extensively studied by measuring the phase coherence [7,9], confirming the universal equation of state [10,11], probing the superfluidity [12], or observing the free vortex proliferation [7,13,14].A 2D interacting Fermi gas at the crossover from a Bose-Einstein condensate (BEC) to a Bardeen-CooperSchrieffer (BCS) superfluid provides a unique platform to address the universal BKT mechanism [15,16], since the underlying character of the system changes from tightly bound composite bosons to loosely bound Cooper pairs of fermions, with decreasing attractions [17]. Indeed, the fermionic BKT transition is now being pursued by several cold-atom laboratories [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35], and there are indications of the transition from the measurements of pair condensation and correlation function, where: (i) the center-of-mass momentum distribution of Cooper pairs, n Q , exhibits anomalous enhancement near Q = 0 below a certain temperature [28], and (ii) the first-order correlation function g 1 (r) in real space decays algebraically [29]. However, confirmation of the transition is still to be demonstrated, as these two features may be explained using a strong-coupling theory in the normal phase [36]. This situation marks the importance of having accurate theoretical predictions for the fermionic BKT transition.The purpose of this Letter is to apply a strong-coupling theory, beyond mean-field, to a 2D interacting Fermi gas in the superfluid phase and present semi-quantitative predictions for the BKT critical chemical potential, critical temperat...

Fermi-to-Bose crossover in a trapped quasi-2D gas of fermionic atoms

“…More important role of the fluctuations in lower dimensions is in agreement with the Ginzburg-Levanyuk criterion [22,23]. Note also that in recent years a considerable numerical effort has been applied to the problem of the BCS-BEC crossover in 2D in the framework of the advanced mean field [21,24], Monte-Carlo simulations [25,26,27,28], and Luttinger-Ward (thermodynamic) identities [29]. Also a generalization of Nozières-Schmitt-Rink approach [9] with gaussian fluctuations to the 2D case was performed [20,30].…”

“…One may see that the Gaussian is off both at the edges and center. For interacting Fermi and Bose gases, the numerical density profiles differ from profile (24). Despite that, since at T = 0 the dependence of the chemical potential on the density is nearly linear (μ ∝ n) [76], the closeness of the density profile to (23) firmly indicates a deep degeneracy and a smallness of the temperature with respect to E F and chemical potentialμ = µ + |E b |/2.…”

Role of the confinement-induced effective range in the thermodynamics of a strongly correlated Fermi gas in two dimensions

“…To consider the BKT transition the superfluid density needs to be calculated for the two-channel model in the superfluid phase, following the work in Ref. [33]. Such a scheme is beyond the scope of this work.…”

Goldstone and Higgs Hydrodynamics in the BCS–BEC Crossover

“…Very recently, the BCS-BEC crossover has also been realized in quasi two-dimensional (2D) configurations [7][8][9][10]. Beyond-mean-field theoretical investigations of 2D Fermi gases in the full BCS-BEC crossover have been carried out both at zero and finite temperature [11][12][13][14][15][16][17]. These 2D results have clearly shown that contrary to the 3D case, mean-field theories are completely unreliable for the study of strongly-interacting superfluid fermions in two dimensions because of the huge increase of quantum fluctuations.…”