Fate of dynamical phases of a BCS superconductor beyond the dissipationless regimen

Abstract

The BCS model of an isolated superconductor initially prepared in a nonequilibrium state, predicts the existence of interesting dynamical phenomena in the time-dependent order parameter as decaying oscillations, persistent oscillations and overdamped dynamics. To make contact with real systems remains an open challenge as one needs to introduce dissipation due to the environment in a self-consistent computation. Here, we reach this goal with the use of the Keldysh formalism to treat the effect of a thermal bath. We show that, contrary to the dissipationless case, all dynamical phases reach the equilibrium order parameter in a characteristic time that depends on the coupling with the bath. Remarkably, as time evolves, the overdamped phase shows a fast crossover where the superconducting order parameter recovers to reach a state with a well-developed long range order that tends towards equilibrium with the damped Higgs mode oscillations. Our results provide a benchmark for the description of the dynamics of real out-of-equilibrium superconductors relevant for quantum technological applications.

7 pages, 3 figures

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Cited by in corpus (14)

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• A cavity-QED quantum simulator of dynamical phases of a BCS superconductor
• Dynamical phases transitions in periodically driven Bardeen-Cooper-Schrieffer systems
• Thermalization of non-Fermi-liquid electron-phonon systems: Hydrodynamic relaxation of the Yukawa-Sachdev-Ye-Kitaev model
• Spectral fingerprints of the non-linear dynamics of driven superconductors with dissipation
• Non-equilibrium dynamics across the BEC-BCS crossover
• Engineering Higgs dynamics by spectral singularities
• Intrinsic dissipative Floquet superconductors beyond mean-field theory
• Generation and decay of Higgs mode in a strongly interacting Fermi gas
• Emergence of Larkin-Ovchinnikov-type superconducting state in a voltage-driven superconductor
• Adiabatic transition from a BCS superconductor to a Fermi liquid and phase dynamics
• Signatures of superconducting Higgs mode in irradiated Josephson junctions
• Attenuating Dynamics of Strongly Interacting Fermionic Superfluids in SYK Solvable Models
• AC Josephson Signatures of the Superconducting Higgs Mode