Dynamical selection in developing fermionic pairing

Abstract

We consider evolution of a Fermi gas in the presence of a time-dependent BCS interaction. The pairing amplitude in the emergent BCS state is found to be an oscillatory function of time with predictable characteristics. The interplay of linear instability of the unpaired state and nonlinear interactions selects periodic soliton trains of a specific form, described by the Jacobi elliptic function dn. While the parameters of the soliton train, such as the period, amplitude, and time lag, fluctuate among different realizations, the elliptic function form remains robust. The parameter variation is accounted for by the fluctuations of particle distribution in the initial unpaired state.Nonequilibrium effects in superconducting systems are usually described using the notion of local equilibrium and quasiparticle distribution [1,2], embodied in the time-dependent Ginzburg-Landau equation [3] or the kinetic equation [4]. The recently studied problem of fast time dynamics in emergent fermionic pairing [5] describing the onset of BCS pairing triggered by an abrupt change of interaction lies somewhat outside this classification. The new aspect of this problem is the absence of a meaningful notion of quasiparticle spectrum. Instead, individual Cooper pair states evolve in a coherent, collisionless fashion [6][7][8][9] independently of the order parameter. The ensuing interesting many-body evolution reflects the system inability to transit adiabatically between the unpaired and paired states due to their vanishing overlap. The oscillatory mode [5] can be viewed as Bloch precession of the pair states in an effective magnetic field defined in terms of the pairing function.Tunable time-dependent pairing interaction can be realized experimentally in ultracold Fermi gases [10][11][12][13]. Fermionic pairing and superfluidity in these systems have been demonstrated recently using magnetically tunable Feshbach resonances [14][15][16]. In these systems, by varying the magnetic field detuning from resonance, both the strength and the sign of inter-particle interaction can be changed on a time scale shorter than the intrinsic times of fermions, set by E F or the elastic collision rate. In Refs. [18,20,21] the picture of time-dependent pairing [5] was extended to the problem of resonant atom-molecule coupling near a Feshbach resonance.Another interesting class of tunable systems are the hybrid semiconductor-superconductor (S/Sm/S) and SNS structures [24][25][26][27][28] with proximity-induced Josephson effect. In the S/Sm/S systems [24,25], the superfluid density and Josephson critical current can be tuned by electric field applied on the gates to the semiconductor. Similarly, the SNS structures [26][27][28] are tunable by current applied to the normal region.Superconductor dynamics is controlled by several kinetic time scales [2]. The most important for us is the collisionless regime [6-9] characterized by the timewith ∆ the equilibrium BCS gap. The time τ ∆ manifests itself in the BCS instability growth rate [7][8][9] at T away from T...

Nonequilibrium pairing instability in ultracold Fermi gases with population imbalance

“…However, as discussed in Ref. 12, a time window for τ 0 exists in which the constraint for avoiding the overheating is compatible with that of a sudden switching-on of the interaction.…”

“…Time-dependent mean-field theory As discussed in Ref. 12, the nonequilibrium evolution of the fermion system can be analyzed within a timedependent mean-field theory. To this end we introduce the pairing function ∆(t) = g k ĉ −k↓ĉk↑ , where the average is taken over the quantum state of the system at time t. After the mean-field decoupling is performed, the BCS Hamiltonian (1) reduces to a sum of time-dependent…”

“…Time-dependent couplings can be realized, for example, by varying the intensity of the laser that fixes the amplitude of an optical lattice or by changing the atomic scattering length through sweeping an external magnetic field across a Feshbach resonance. This problem, which has attracted a lot of attention recently [4,5,6,7,8,9,10,11,12,13,14,15,16,17,18], is what we consider as well.…”

“…Guided by the body of knowledge acquired in the study of the equilibrium case, one can look also for instabilities towards more complex paired states that we leave for future study. The time scales that are relevant to the present problem [12] are the quasiparticle Landau Fermi-liquid lifetime τ el , the time τ ∆ over which the oscillations of the pairing function develop and evolve [5], and the characteristic time τ 0 over which the coupling is switched on. We are interested in the regime when the inequalities τ 0 τ ∆ < t τ el hold.…”

Quantum quench phase diagrams of ans-wave BCS-BEC condensate

“…Recent studies, motivated by experiments in cold atomic fermions, focused on quantum quenches, nonequilibrium conditions created by a sudden change in the superconducting coupling strength. Barankov et al [7], in a paper that set off a surge of modern research in this long-standing problem [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] in the context of quantum gases, found that for initial conditions close to the unstable normal state, the order parameter exhibits large anharmonic periodic oscillations.…”