Generalized Quasi-Energies and Floquet States for a Dissipative System

Zhuocheng Ma, Hongzheng Zhao, Liang-You Peng

Static coupling to a dissipative cavity has been proposed as a route to autonomously stabilize Floquet eigenstates. The cavity provides an energy-selective relaxation channel: when its photon energy matches a quasienergy difference modulo drive quanta, it mediates transitions between Floquet states, followed by irreversible photon loss. Here, we show that at intermediate driving frequencies, this resonance condition alone is not sufficient for stabilization. Instead, the steady state is controlled by the interplay between resonance selection and the cavity-induced transition strengths between Floquet states, which can either cooperate or compete. This interplay leads to successful stabilization, mixed steady states despite resonance, and complete breakdown near Floquet-zone hybridization. We further show that the same mechanism extends to multilevel spin-S systems, providing a general framework for understanding when static dissipation can reliably stabilize driven quantum states.

Karthik Seetharam, Charles-Edouard Bardyn, Netanel H. Lindner +2 more

Tatsuhiko Shirai, Juzar Thingna, Takashi Mori +3 more

A periodically driven quantum system, when coupled to a heat bath, relaxes to a non-equilibrium asymptotic state. In the general situation, the retrieval of this asymptotic state presents a rather non-trivial task. It was recently shown that in the limit of an infinitesimal coupling, using the so-called rotating wave approximation (RWA), and under strict conditions imposed on the time-dependent system Hamiltonian, the asymptotic state can attain the Gibbs form. A Floquet–Gibbs state is characterized by a density matrix which is diagonal in the Floquet basis of the system Hamiltonian with the diagonal elements obeying a Gibbs distribution, being parametrized by the corresponding Floquet quasi-energies. Addressing the non-adiabatic driving regime, upon using the Magnus expansion, we employ the concept of a corresponding effective Floquet Hamiltonian. In doing so we go beyond the conventionally used RWA and demonstrate that the idea of Floquet–Gibbs states can be extended to the realistic case of a weak, although finite system-bath coupling, herein termed effective Floquet–Gibbs states.

Karthik Seetharam, Charles-Edouard Bardyn, Netanel H. Lindner +2 more

Xiaobing Luo, Liping Li, Li You +1 more

We study a system of three coherently coupled states, where one state is shifted periodically against the other two. We discover that this system possesses a dark Floquet state that has zero quasi-energy and negligible population at the intermediate state. This dark Floquet state manifests itself dynamically in terms of the suppression of inter-state tunneling, a phenomenon known as coherent destruction of tunneling (CDT). Owing to its different origin from the CDT found in a two-state-driven system, we call it dark CDT. At a high-frequency limit for the periodic driving, this Floquet state reduces to the well-known dark state. Our results can be generalized to systems with more states and be verified with easily implemented experiments within the current technologies.

Karthik Seetharam, Charles-Edouard Bardyn, Mark Spencer Rudner +2 more