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

HECTOR PABLO OJEDA COLLADO; GONZALO USAJ; CARLOS A. BALSEIRO; DAMIÁN ZANETTE; JOSÉ LORENZANA

Physical Review Research

APS

Año: 2021 vol. 3 p. 42023 - 42023

2643-1564

We study the out-of-equilibrium dynamics of a Bardeen-Cooper-Schrieffer condensate subject to a periodicdrive. We demonstrate that the combined effect of drive and interactions results in emerging parametricresonances, analogous to a vertically driving pendulum. In particular, Arnold tongues appear when the drivingfrequency matches 2Delta_0/n, with n being a natural number and Delta_0 being the equilibrium gap parameter. Insidethe Arnold tongues we find a commensurate time-crystal condensate which retains the U(1) symmetry breakingof 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 withoutthe need of a strong perturbation. Our results are directly relevant to cold-atom and condensed-matter systemsand do not require very long energy relaxation times to be observed.