Dynamical Vanishing of the Order Parameter in a Fermionic Condensate

Abstract

We analyze the dynamics of a condensate of ultra-cold atomic fermions following an abrupt change of the pairing strength. At long times, the system goes to a non-stationary steady state, which we determine exactly. The superfluid order parameter asymptotes to a constant value. We show that the order parameter vanishes when the pairing strength is decreased below a certain critical value. In this case, the steady state of the system combines properties of normal and superfluid statesthe gap and the condensate fraction vanish, while the superfluid density is nonzero.Recently, several remarkable experiments have demonstrated Cooper pairing in cold atomic Fermi gases [1][2][3][4]. Key signatures of a paired state -condensation of Cooper pairs [1,2] and the pairing gap [4] have been observed. In addition, trapped gases provide a unique tool to explore aspects of fermion pairing normally inaccessible in superconductors. One of the most exciting prospects is a study of far from equilibrium coherent dynamics of fermionic condensates [5][6][7][8][9], made possible due to the precise experimental control over interactions between atoms [10,11]. The dynamics can be initiated by quickly changing the pairing strength with external magnetic field.In the present paper, we determine the time evolution of a fermionic condensate in response to a sudden change of interaction strength. Initially, the gas is in equilibrium at zero temperature on the BCS side of the Feshbach resonance with a coupling constant g i > 0. At t = 0 the coupling is suddenly changed to a smaller value g f > 0 on the same side of the resonance, g i → g f , Fig. 1 (inset). Ground states of the system at the old, g i , and new, g f , values of the coupling are characterized by corresponding BCS gaps, ∆ i and ∆ f , respectively. We consider the case ∆ i ≥ ∆ f . It has been shown previously that following the change of coupling, the time-dependent order parameter ∆(t) asymptotes to a constant value [9], |∆(t)| → ∆ ∞ on a timescale τ ∆ = 1/∆ i . Here we evaluate ∆ ∞ in terms of ∆ i and ∆ f .We show that when the coupling is decreased below a certain critical value, ∆ ∞ vanishes, Fig. 1. On a τ ∆ timescale the system goes to a steady non-stationary state that combines properties of normal and superfluid states in a peculiar way. For example, the gap vanishes, while the superfluid density remains finite. Provided the system is continuously cooled, the BCS ground state with a gap ∆ f is reached on the energy relaxation timescale τ ǫ , which is typically much larger than τ ∆ . Experimental signatures of the novel state include the absence of the gap in rf absorbtion spectrum and zero condensate fraction after a fast projection onto the Bose-Einstein Condensation (BEC) side (see below).At times t ≪ τ ǫ , dynamics of the condensate in the weak coupling regime can be described by theTime evolution of the BCS order parameter ∆(t) following an abrupt change of the coupling constant. The coupling is changed by varying the magnetic field on the BCS side of the Feshbach reso...

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