Emergent parametric resonances and time-crystal phases in driven BCS 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 $2{\Delta }_0/n$, 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.

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• A Decade of Time Crystals: Quo Vadis?
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• Fractional resonances and prethermal states in Floquet systems
• Equilibrium Parametric Amplification in Raman-Cavity Hybrids
• Theory of parametric resonance for discrete time crystals in fully-connected spin-cavity systems
• Time-crystalline behavior in central-spin models with Heisenberg interactions
• Exciting the long-lived Higgs mode in superfluid Fermi gases with particle removal
• Adiabatic transition from a BCS superconductor to a Fermi liquid and phase dynamics
• Steering spin fluctuations in lattice systems via two-tone Floquet engineering
• Quenched dynamics and pattern formation in clean and disordered Bogoliubov-de Gennes superconductors
• Emergence of spatial patterns and synchronization in superconducting time crystals
• Stable many-body resonances in open quantum systems
• Information scrambling and entanglement dynamics in Floquet Time Crystals
• Controlled bit-flip of period-doubling and discrete time crystalline states in open systems
• Many-body correlations in Floquet steady-states: Frequency-resolved renormalization group of the driven Anderson impurity