Emergent parametric resonances and time-crystal phases in driven Bardeen-Cooper-Schrieffer systems

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 2Δ0/n, with n being a natural number and Δ0 being 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.Received 28 July 2021Revised 15 October 2021Accepted 19 October 2021DOI:https://doi.org/10.1103/PhysRevResearch.3.L042023Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasDynamical phase transitionsExotic phases of matterNonequilibrium statistical mechanicsSuperconductivitySuperfluiditySynchronizations-wavePhysical SystemsFloquet systemsUltracold gasesTechniquesBCS theoryMethods in superconductivityCondensed Matter, Materials & Applied PhysicsNonlinear Dynamics