Floquet dynamics of classical and quantum cavity fields

Abstract

We show that the time-dependence of electromagnetic field in a parametrically modulated cavity can be effectively analyzed using a $Floquet$ $map$. The map relates the field states separated by one period of the drive; iterative application of the map allows to determine field configuration after arbitrary number of drive periods. For resonant and near-resonant drives, the map has stable and unstable fixed points, which are the loci of infinite energy concentration in the long time limit. The Floquet map method can be applied both to classical and quantum massless field problems, including the dynamical Casimir effect. The stroboscopic time evolution implemented by the map can be interpreted in terms of the wave propagation in a curved space, with the fixed points of the map corresponding to the black hole and white hole horizons. More practically, the map can be used to design protocols for signal compression/decompression, cooling, and sensing.

21 pages; added new Appendix B: derivation of (semiclassical) Floquet dynamics for a classical field in a fixed cavity with a spatiotemporally modulated medium inside

References in corpus (6)

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• Observation of discrete time-crystalline order in a disordered dipolar many-body system
• Floquet Time Crystals
• General Relativity in Electrical Engineering
• Absence of Quantum Time Crystals
• Comment on "Quantum Time Crystals": a new paradigm or just another proposal of perpetuum mobile?

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• Floquet conformal field theories with generally deformed Hamiltonians
• Classification of $S{L}_2$ deformed Floquet Conformal Field Theories
• Periodically, Quasi-periodically, and Randomly Driven Conformal Field Theories (II): Furstenberg's Theorem and Exceptions to Heating Phases
• From the moving piston to the dynamical Casimir effect: explorations with shaken condensates
• Floquet engineered inhomogeneous quantum chaos in critical systems
• Inhomogeneous Quantum Quenches of Conformal Field Theory with Boundaries
• Non-dispersing wave packets in lattice Floquet systems
• Direct driving of electronic and phononic degrees of freedom in a honeycomb bilayer with infrared light