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arXiv:1411.0429 · Physical Review A

Superradiant phase transition of Fermi gases in a cavity across a Feshbach resonance

Yu Chen, Hui Zhai, Zhenhua Yu

Published Feb 19, 2015• 30 citations
arXivHTMLPDF

Abstract

We consider the superradiant phase transition of a two-component Fermi gas in a cavity across a Feshbach resonance. It is known that quantum statistics plays a crucial role for the superradiant phase transition in atomic gases; in contrast to bosons, in a Fermi gas this transition exhibits strong density dependence. We show that across a Feshbach resonance, while the two-component Fermi gas passes through the BEC-BCS crossover, the superradiant phase transition undergoes a corresponding crossover from a fermionic behavior on the weakly interacting BCS side, to a bosonic behavior on the molecular Bose-Einstein condensate (BEC) side. This intricate statistics crossover makes the superradiance maximally enhanced either in the unitary regime for low densities, in the BCS regime for moderate densities close to Fermi surface nesting, or in the BEC regime for high densities.

DOI
10.1103/physreva.91.021602

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We consider the superradiant phase transition of a two-component Fermi gas in a cavity across a Feshbach resonance. It is known that quantum statistics plays a crucial role for the superradiant phase transition in atomic gases; in contrast to bosons, in a Fermi gas this transition exhibits strong density dependence. We show that across a Feshbach resonance, while the two-component Fermi gas passes through the BEC-BCS crossover, the superradiant phase transition undergoes a corresponding crossover from a fermionic behavior on the weakly interacting BCS side, to a bosonic behavior on the molecular Bose-Einstein condensate (BEC) side. This intricate statistics crossover makes the superradiance maximally enhanced either in the unitary regime for low densities, in the BCS regime for moderate densities close to Fermi surface nesting, or in the BEC regime for high densities.
In this Rapid Communication a generalization of the BEC-BCS crossover theory to a multicomponent superfluid is presented by studying a three-species mixture of Fermi gas across two Feshbach resonances. At the BEC side of resonances, two kinds of molecules are stable which gives rise to a two-component Bose condensate. This two-component superfluid state can be experimentally identified from the radio-frequency spectroscopy, density profile, and short noise measurements. As approaching the BCS side of resonances, the superfluidity will break down at some point and yield a first-order quantum phase transition to normal state, due to the mismatch of three Fermi surfaces. Phase separation instability will occur around the critical regime.
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 investigate strong-coupling effects on the superfluid phase transition in a gas of Fermi atoms with a Feshbach resonance. The Feshbach resonance describes a composite quasiboson that can give rise to an additional pairing interaction between the Fermi atoms. This attractive interaction becomes stronger as the threshold energy $2\ensuremath{\nu}$ of the Feshbach resonance two-particle bound state is lowered. In a recent paper, we showed that in the uniform Fermi gas, this tunable pairing interaction naturally leads to a crossover from a BCS state to a Bose-Einstein condensate (BEC) of the Nozi\`eres and Schmitt-Rink kind, in which the BCS-type superfluid phase transition continuously changes into the BEC type as the threshold energy is decreased. In this paper, we extend our previous work by including the effect of a harmonic trap potential, treated within the local-density approximation. We also give results for both weak and strong coupling to the Feshbach resonance. We show that the BCS-BEC crossover phenomenon strongly modifies the shape of the atomic density profile at the superfluid phase-transition temperature Tc,{T}_{\mathrm{c}},Tc​, reflecting the change of the dominant particles going from Fermi atoms to composite bosons. In the BEC regime, these composite bosons are shown to first appear well above Tc.{T}_{\mathrm{c}}.Tc​. We also discuss the ``phase diagram'' above Tc{T}_{\mathrm{c}}Tc​ as a function of the tunable threshold energy $2\ensuremath{\nu}.$ We introduce a characteristic temperature ${T}^{*}(2\ensuremath{\nu})$ describing the effective crossover in the normal phase from a Fermi gas of atoms to a gas of stable molecules.
We investigate strong-coupling superfluidity in a uniform two-component gas of ultracold Fermi atoms attractively interacting via quasimolecular bosons associated with a Feshbach resonance. This interaction is tunable by the threshold energy $2\ensuremath{\nu}$ of the Feshbach resonance, becoming large as $2\ensuremath{\nu}$ is decreased (relative to $2{\ensuremath{\varepsilon}}_{\mathrm{F}},$ where ${\ensuremath{\varepsilon}}_{\mathrm{F}}$ is the Fermi energy of one component). In recent work, we showed that the enhancement of this tunable pairing interaction naturally leads to the BCS-BEC (Bose-Einstein condensation) crossover, where the character of the superfluid phase transition changes from the BCS type to a BEC of composite bosons consisting of preformed Cooper-pairs and Feshbach-induced molecules. In this paper, we extend our previous work and study both the quasiparticles and the collective dynamics of the superfluid phase below the phase-transition temperature Tc,{T}_{\mathrm{c}},Tc​, limiting ourselves to a uniform gas. We show how the superfluid order parameter changes from the Cooper-pair amplitude $\ensuremath{\Delta}$ to the square root of the number of condensed molecules $({\ensuremath{\varphi}}_{\mathrm{m}})$ associated with the Feshbach resonance, as the threshold energy $2\ensuremath{\nu}$ is lowered. In the intermediate coupling regime, the superfluidity is shown to be characterized by an order parameter consisting of a superposition of $\ensuremath{\Delta}$ and ${\ensuremath{\varphi}}_{\mathrm{m}}.$ We also discuss the Goldstone mode associated with superfluidity, and show how its character smoothly changes from the Anderson-Bogoliubov phonon in the BCS regime to the Bogoliubov phonon in the BEC regime in the BCS-BEC crossover. The velocity of this Goldstone phonon mode is shown to strongly depend on the value of $2\ensuremath{\nu}.$ We also show that this Goldstone mode appears as a resonance in the spectrum of the density-density correlation function, which is experimentally accessible.
We consider a single vortex in a superfluid Fermi gas in the BCS-BEC crossover regime near a Feshbach resonance. The effect of the molecular Bose-Einstein condensate upon the vortex structure is discussed within the mean field approximation at zero temperature. Using the self-consistent Bogoliubov-de Gennes equation of the fermion-boson coupled model, we calculate density distributions of atoms and molecules. As the number of the molecules increases, both atomic and molecular density changes from BCS-like distribution to BEC-like. We also study the change of the vortex core size in the crossover regime.
This thesis presents experiments probing physics in the crossover between Bose-Einstein condensation (BEC) and BCS superconductivity using an ultracold gas of atomic fermions. Scattering resonances in these ultracold gases (known as Feshbach resonances) provide the unique ability to tune the fermion-fermion interactions. The work presented here pioneered the use of fermionic Feshbach resonances as a highly controllable and tunable system ideal for studying the cusp of the BCS-BEC crossover problem. Here pairs of fermionic atoms have some properties of diatomic molecules and some properties of Cooper pairs. I present studies of a normal Fermi gas at a Feshbach resonance and the work required to cool the gas to temperatures where superfluidity in the crossover is predicted. These studies culminated in our observation of a phase transition at the cusp of the BCS-BEC crossover through condensation of fermionic atom pairs. I also discuss subsequent work that confirmed the crossover nature of the pairs in these condensates.