Period-doubling in period-$1$ steady states

TL;DR

This paper demonstrates that a many-body open quantum system can exhibit period-doubling in its steady state, revealing quantum signatures of classical nonlinear phenomena and suggesting potential for Floquet time crystals.

Contribution

It introduces a method to detect period-doubling in quantum steady states via spectral analysis and correlations, bridging classical chaos and quantum dynamics.

Findings

Quantum steady state shows period-doubling signatures

Spectral analysis reveals eigenvalues indicating period-doubling

Potential realization as Floquet time crystals

Abstract

Nonlinear classical dissipative systems present a rich phenomenology in their "route to chaos", including period-doubling, i.e. the system evolves with a period which is twice that of the driving. However, typically the attractor of a periodically driven quantum open system evolves with a period which exactly matches that of the driving. Here we analyze a manybody open quantum system whose classical correspondent presents period-doubling. We show that by analysing the spectrum of the periodic propagator and by studying the dynamical correlations, it is possible to show the occurrence of period-doubling in the quantum (period-$1$) steady state. We also discuss that such systems are natural candidates for clean Floquet time crystals.