Floquet dynamics of classical and quantum cavity fields

TL;DR

This paper introduces a Floquet map approach to analyze the time evolution of classical and quantum cavity fields under parametric modulation, revealing stable and unstable fixed points and applications to signal processing and quantum effects.

Contribution

It develops a Floquet map framework for cavity field dynamics applicable to both classical and quantum regimes, including the dynamical Casimir effect.

Findings

Floquet map relates field states across drive periods.

Stable and unstable fixed points correspond to energy concentration.

Applications include signal compression, cooling, and sensing.

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.