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  • Letter
  • Open Access

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

H. P. Ojeda Collado1,2,3,*, Gonzalo Usaj2,3, C. A. Balseiro2,3, Damián H. Zanette2,4, and José Lorenzana1,†

  • 1ISC-CNR and Department of Physics, Sapienza University of Rome, Piazzale Aldo Moro 2, I-00185, Rome, Italy
  • 2Centro Atómico Bariloche and Instituto Balseiro, Comisión Nacional de Energía Atómica (CNEA)–Universidad Nacional de Cuyo (UNCUYO), 8400 Bariloche, Argentina
  • 3Instituto de Nanociencia y Nanotecnología (INN), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET)–CNEA, 8400 Bariloche, Argentina
  • 4Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Argentina

  • *hector.pablo.ojedacollado@roma1.infn.it
  • †jose.lorenzana@cnr.it
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Phys. Rev. Research 3, L042023 – Published 10 November, 2021

DOI: https://doi.org/10.1103/PhysRevResearch.3.L042023

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.

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Phys. Rev. Research 3, L042023– Published 10 November, 2021
  • Received 28 July 2021
  • Revised 15 October 2021
  • Accepted 19 October 2021
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