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

• Published in: Physical review research Vol. 3; no. 4; p. L042023
• Main Authors: Ojeda Collado, H. P., Usaj, Gonzalo, Balseiro, C. A., Zanette, Damián H., Lorenzana, José
• Format: Journal Article
• Language: English
• Published: American Physical Society 01.11.2021
• ISSN: 2643-1564; 2643-1564
• DOI: 10.1103/PhysRevResearch.3.L042023

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 2Δ_{0}/n, with n being a natural number and Δ_{0} 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.