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Acta Physica Sinica

Density profile of a superfluid Fermi gas with a phase slip

Hong-Yu Wu, Yin Lan, 北京大学物理学院，北京 100871

Published Jan 1, 2006• 5 citations
Publisher

Abstract

BEC(Bose Einstein Condensation)-BCS(Bardeen Schrieffer Cooper) crossover is currently one of the main research focuses in the area of cold atoms and BEC. In this paper, we study in detail the phenomenon of a phase slip in a superfluid Fermi gas near a Feshbach resonance, based on our previous work. The density profiles of a superfluid Fermi gas with a phase slip at various temperatures are computed by numerical method. Our results show that the phase-slip phenomenon can provide a direct experimental evidence of the superfluid phase.

DOI
10.7498/aps.55.490

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BEC(Bose Einstein Condensation)-BCS(Bardeen Schrieffer Cooper) crossover is currently one of the main research focuses in the area of cold atoms and BEC. In this paper, we study in detail the phenomenon of a phase slip in a superfluid Fermi gas near a Feshbach resonance, based on our previous work. The density profiles of a superfluid Fermi gas with a phase slip at various temperatures are computed by numerical method. Our results show that the phase-slip phenomenon can provide a direct experimental evidence of the superfluid phase.
We study the properties of a phase slip in a superfluid Fermi gas near a Feshbach resonance. The phase slip can be generated by the phase imprinting method. Below the superfluid transition temperature, it appears as a dip in the density profile and becomes more pronounced when the temperature is lowered. Therefore the phase slip can provide direct evidence of the superfluid state. The condensation energy of the superfluid state can be extracted from the density profile of the phase slip, due to the unitary properties of the Fermi gas near the resonance. The width of the phase slip is inversely proportional to the square root of the difference between the transition temperature and the temperature. The signature of the phase slip in the density profile becomes more robust across the BCS-Bose-Einstein-condensate crossover.
We investigate the Bose-Einstein condensation of fermionic pairs in a uniform two-component Fermi gas, obtaining an explicit formula for the condensate density as a function of the chemical potential and the energy gap. We analyze the condensate fraction in the crossover from the Bardeen-Cooper-Schrieffer (BCS) state of weakly interacting Cooper pairs to the Bose-Einstein condensate of molecular dimers. By using the local-density approximation we study confined Fermi vapors of alkali-metal atoms for which there is experimental evidence of condensation also on the BCS side of the Feshbach resonance. Our theoretical results are in agreement with these experimental data and give the behavior of the condensate on both sides of the Feshbach resonance at zero temperature.
We discuss the superfluid phase transition in a gas of Fermi atoms with a Feshbach resonance. A tunable pairing interaction associated with the Feshbach resonance is shown to naturally lead to the BCS-BEC crossover, where the character of superfluidity continuously changes from the weak-coupling Bardeen-Cooper-Schrieffer (BCS) type to the Bose-Einstein condensation (BEC) of tightly bound molecules, as one decreases the threshold energy 2ν of the Feshbach resonance. We also discuss effects of a trap, as well as the p-wave BCS-BEC crossover adjusted by a p-wave Feshbach resonance.
PACS. 03.75.Hh – Static properties of condensates; thermodynamical, statistical and structural properties. PACS. 03.75.Ss – Degenerate Fermi gases. PACS. 05.30.Fk – Fermion systems and electron gas. Abstract. – We present a theory for a superfluid Fermi gas near the BCS-BEC crossover, including pairing fluctuation contributions to the free energy similar to that considered by Nozières and Schmitt-Rink for the normal phase. In the strong coupling limit, our theory is able to recover the Bogoliubov theory of a weakly interacting Bose gas with a molecular scattering length very close to the known exact result. We compare our results with recent Quantum Monte Carlo simulations both for the ground state and at finite temperature. Excellent agreement is found for all interaction strengths where simulation results are available. The recent experimental realization of strongly interacting Fermi gases of 6 Li and 40 K atoms near a Feshbach resonance has opened up the exciting possibility of investigating the crossover from a Bardeen-Cooper-Schrieffer (BCS) superfluid to a Bose-Einstein condensate (BEC) [1–5]. In these systems, the inter-atomic interaction strength can be varied by tuning
We investigate unconventional superfluidity in a gas of Fermi atoms with an anisotropic p-wave Feshbach resonance. Including the p-wave Feshbach resonance as well as the associated three kinds of quasimolecules with finite orbital angular momenta Lz=+/-1,0, we calculate the transition temperature of the superfluid phase. As one passes through the p-wave Feshbach resonance, we find the usual BCS-BEC crossover phenomenon. The p-wave BCS state continuously changes into the BEC of bound molecules with L=1. Our calculation includes the effect of fluctuations associated with Cooper pairs and molecules which are not Bose condensed.
We show that the thermodynamic properties of an atomic Fermi gas near the unitarity limit for Feshbach scattering is not universal as long as the resonance is narrow on the scale of the Fermi energy. In view of ongoing quantum Monte Carlo simulations, we explore this behavior within a mean-field approach extended to a finite temperature by means of a model potential, which allows for a tuning of the scattering phase shift and its energy dependence. Our results may be relevant for constructing a complete theoretical description of the crossover from a Bose-Einstein condensation (BEC) of composite bosons to a Bardeen-Cooper-Schrieffer (BCS) of Cooper pairs.