Path-integral mean-field description of the vortex state in the BEC-to-BCS crossover

Abstract

We derive a path-integral description of the vortex state of a fermionic superfluid in the crossover region between the molecular condensate (BEC) regime and the Cooper pairing (BCS) regime.This path-integral formalism, supplemented by a suitable choice for the saddle point value of the pairing field in the presence of a vortex, offers a unified description that encompasses both the BEC and BCS limits. The vortex core size is studied as a function of the tunable interaction strength between the fermionic atoms. We find that in the BEC regime, the core size is determined by the molecular healing length, whereas in the BCS regime, the core size is proportional only to the Fermi wave length. The observation of such quantized vortices in dilute Fermi gases would provide an unambiguous proof of the realization of superfluidity in these gases.

When are two fermions a simple boson? New Gross–Pitaevskii actions for cold Fermi condensates

“…Thus, technically, we should only believe the vortex solution from(99) away from the vortex core where F ≈ 1. In practice, since F has to vanish at the core, we anticipate the vortex solution of Fig.1 to have greater validity [22]. In this regard there are some similarities with [22], although in our case the density is entirely diatomic.…”

“…In practice, since F has to vanish at the core, we anticipate the vortex solution of Fig.1 to have greater validity [22]. In this regard there are some similarities with [22], although in our case the density is entirely diatomic. However, unlike the approach of [22], in our case a new Gross-Pitaevskii action for the BEC regime is constructed with a clear Galilean identification of coupled fields as dimers.…”

“…Nonetheless, it is worth showing the relationship since it is not uncommon (e.g. [22,23]) to see derivative expansions in fluctuation fields despite Galilean invariance being crucial to some attributes of the quantum behaviour (e.g. the stochastic nature of the sound-cone metric [24]).…”

Solutions of Ginzburg-Landau theory for atomic Fermi gases near the BCS-BEC crossover

“…In the superfluid atomic Fermi gases near the Feshbach resonance the strong attractive interaction is realized between fermion atoms, which can cause the BCS-BEC crossover [8,10,13] . To our knowledge the GL theory has not yet been fully studied in the BCS-BEC crossover regime except for a few pioneering works [4,6] and recent related ones [2,5,12,14] in the single-component fermion systems (single channel model). Though rich research has been done in the TDGL equation derived from the single-channel model [7,11] .…”

Vortex properties of a resonant superfluid

“…The vortex structure in superfluid fermi gas have been studied theoretically [11,12,13,14,15,16,17,18]. However most of these works focus on the non-rotating case, which is different from the experimental situation.…”