Emergent parametric resonances and time-crystal phases in driven BCS systems

TL;DR

This paper investigates how periodic driving induces parametric resonances and time-crystal phases in BCS superconductors, revealing new dynamical states and symmetry-breaking phenomena observable in cold-atom and condensed matter systems.

Contribution

It demonstrates the emergence of parametric resonances and time-crystal phases in driven BCS systems, highlighting the formation of Arnold tongues and symmetry-breaking states without long relaxation times.

Findings

Parametric resonances occur at specific driving frequencies related to the equilibrium gap.

Time-crystal condensates exhibit additional time-translational symmetry breaking.

Synchronized Higgs modes are stabilized outside Arnold tongues.

Abstract

We study the out-of-equilibrium dynamics of a Bardeen-Cooper-Schrieffer condensate subject to a periodic drive. We demonstrate that the combined effect of drive and interactions results in emerging parametric resonances, analogous to a vertically driving pendulum. In particular, Arnold tongues appear when the driving frequency matches $2\Delta_0/n$, with $n$ a natural number, and $\Delta_0$ the equilibrium gap parameter. Inside the Arnold tongues we find a commensurate time-crystal condensate which retains the $U(1)$ symmetry breaking of the parent superfluid/superconducting phase and shows an additional time-translational symmetry breaking. Outside these tongues, the synchronized collective Higgs mode found in quench protocols is stabilized without the need of a strong perturbation. Our results are directly relevant to cold-atom and condensed-matter systems and do not require very long energy relaxation times to be observed.