Pairing in two-dimensional Fermi gases with a coordinate-space potential

Abstract

In this work we theoretically study pairing in two-dimensional Fermi gases, a system which is experimentally accessible using cold atoms. We start by deriving the mean-field pairing gap equation for a coordinate-space potential with a finite interaction range, and proceed to solve this numerically. We find that for sufficiently short effective ranges the answer is identical to the zero-range one. We then use Diffusion Monte Carlo to evaluate the total energy for many distinct particle numbers; we employ several variational parameters to produce a good ground-state energy and then use these results to extract the pairing gap across a number of interaction strengths in the strongly interacting two-dimensional crossover. Extracting the gap via the odd-even energy staggering, our microscopic results can be used as benchmarks for other theoretical approaches.

Comparing fermionic superfluids in two and three dimensions

“…When comparing these results to theory, we find that they are in excellent agreement with mean-field theory [28] in the BCS regime, but begin to deviate from the mean-field results in the strongly correlated crossover region (ln(k F a 2D ) ≈ 1). Quantum Monte-Carlo (QMC) simulations [29,30] are in somewhat better agreement with our data in the crossover, but still predict larger values of ∆ − E B /2 in the BEC regime.…”

“…The data appears to be well-described by theoretical predictions for threedimensional fermionic superfluids [35], but as shown in Fig. 2d deviates from 2D QMC calculations [29,30]. This is unlikely to be the result of imperfect two-dimensional confinement or thermal excitations, which would both be expected to have the strongest effect in the BCS regime (see Supplementary Materials).…”

“…Superfluid gap ∆/EF of two-dimensional (blue circles and diamonds) and threedimensional (red stars) Fermi gases as a function of the chemical potential µ/EF, for which we use the results of QMC calculations [33,34]. The measurements of the gap collapse onto a single curve, which is well-described by theoretical predictions for the gap in three-dimensional Fermi gases (red line [35,36]); results from 2D QMC calculations [29,30] are shown as gray diamonds (see Supplementary Materials). Error bars denote 1σ confidence intervals of the fit.…”

“…BEC-BCS mean field predictions (dashed orange line, [28]) are in agreement with our measurement in the BCS regime, but deviate in the strongly correlated crossover regime. Quantum Monte-Carlo calculations (gray triangles, [29,30]) show better agreement in the crossover, but still deviate from the measurements in the BEC regime. Error bars denote 1σ confidence intervals of the fit and are smaller than the symbol size, the data shown in panels a (b) is the average of 8 (26) individual measurements.…”

The 1S0 Pairing Gap in Neutron Matter

“…Strongly interacting cold Fermi atoms have been the subject of many theoretical investigations [11][12][13][14][15][16][17][18]. Experimentally, they have been studied extensively since the beginning of the century, owing in part, to the simplicity of these experiments compared to those for their bosonic counterparts [2].…”