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.
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.
Strong periodic driving of cavity-quantum electrodynamics (QED) in the ultrastrong-coupling regime creates nonequilibrium states whose dissipation is governed by Floquet quasienergies rather than undriven dressed resonances. However, modeling such a regime is a significant theoretical challenge, including a number of subtle problems such as the need to ensure gauge invariance for truncated matter-cavity systems with time-dependent driving. To fill this theoretical gap, we introduce a nonsecular Floquet generalized master equation framework for strongly driven open cavity-QED systems, formulated in the dressed basis of the quantum Rabi model and applicable to structured reservoirs without rotating-wave approximations. Our theory can thus model Floquet-driven dynamics in open ultrastrong-coupling cavity-QED, and demonstrates a wide range of quantum state control. Using strong optical pumping and parametric mechanical modulation, we compute long-time populations, fluorescence spectra, and the Floquet-Liouville eigenspectra, resolving observable resonances into hybridized quasienergy channels and decay rates. By systematically comparing with conventional time-independent dressed-basis generalized master equations, we show that static approaches only reproduce steady-state populations in restricted excitation regimes, and fail for frequency-resolved observables and break down under appropriate Floquet engineering, surprisingly, even for spectrally flat baths. Structured environments, such as Lorentzian-Ohmic reservoirs, further amplify these discrepancies through sideband-selective decay. Our results demonstrate that dissipation in driven ultrastrong cavity-QED is intrinsically quasienergy resolved and we establish Floquet-dissipative theory as an accurate and powerful framework for predicting spectra, controlling decay pathways, and engineering nonequilibrium quantum states and reservoirs.
Floquet engineering, in which the properties of a quantum system are modified through the application of strong periodic drives, is an indispensable tool in atomic and condensed matter systems. However, it is inevitably limited by intrinsic heating processes. We describe a simple autonomous scheme, which exploits a coupling between the driven system and a lossy auxiliary, to cool large classes of Floquet systems into desired states. We present experimental and theoretical evidence for the stabilization of a chosen state in a strongly modulated transmon qubit coupled to an auxiliary microwave cavity with fixed frequency and photon loss. The scheme naturally extends to Floquet systems with multiple degrees of freedom. As an example, we demonstrate the stabilization of topological photon pumping in a driven cavity-QED system numerically. The coupling to the auxiliary cavity increases the average photon current and the fidelity of nonclassical states, such as high-photon-number Fock states, that can be prepared in the system cavity.
Abstract We theoretically investigate basic properties of nonequilibrium steady states of periodically-driven open quantum systems based on the full solution of the Maxwell–Bloch equation. In a resonant driving condition, we find that the transverse relaxation, also known as decoherence, significantly destructs the formation of Floquet states while the longitudinal relaxation does not directly affect it. Furthermore, by evaluating the quasienergy spectrum of the nonequilibrium steady states, we demonstrate that Rabi splitting can be observed as long as the decoherence time is as short as one third of the Rabi-cycle. Moreover, we find that Floquet states can be formed even under significant dissipation when the decoherence time is substantially shorter than the cycle of driving, once the driving field strength becomes strong enough. In an off-resonant condition, we demonstrate that the Floquet states can be realized even in weak field regimes because the system is not excited and the decoherence mechanism is not activated. Once the field strength becomes strong enough, the system can be excited by multi-photon absorption and the decoherence process becomes active. As a result, the Floquet states are significantly disturbed by the environment even in the off-resonant condition. Thus, we show here that the suppression of energy transfer from light to matter is a key condition for the realization of Floquet states in both on- and off-resonant conditions not only because it prevents material damage but also because it contributes to preserving coherence.
We theoretically investigate basic properties of nonequilibrium steady states of periodically-driven open quantum systems based on the full solution of the Maxwell–Bloch equation. In a resonant driving condition, we find that the transverse relaxation, also known as decoherence, significantly destructs the formation of Floquet states while the longitudinal relaxation does not directly affect it. Furthermore, by evaluating the quasienergy spectrum of the nonequilibrium steady states, we demonstrate that Rabi splitting can be observed as long as the decoherence time is as short as one third of the Rabi-cycle. Moreover, we find that Floquet states can be formed even under significant dissipation when the decoherence time is substantially shorter than the cycle of driving, once the driving field strength becomes strong enough. In an off-resonant condition, we demonstrate that the Floquet states can be realized even in weak field regimes because the system is not excited and the decoherence mechanism is not activated. Once the field strength becomes strong enough, the system can be excited by multi-photon absorption and the decoherence process becomes active. As a result, the Floquet states are significantly disturbed by the environment even in the off-resonant condition. Thus, we show here that the suppression of energy transfer from light to matter is a key condition for the realization of Floquet states in both on- and off-resonant conditions not only because it prevents material damage but also because it contributes to preserving coherence.
Periodically driven quantum systems are commonly modeled using master equations constructed in the eigenbasis of an undriven Hamiltonian, implicitly assuming that environmental dissipation couples to static energy transitions even under strong time-periodic driving. The validity of this approximation beyond weak or near-resonant driving remains poorly understood. To address the need for a more self-consistent quantum theory approach, we formulate a nonsecular Floquet--Markov generalized master equation (F-GME) in the quasienergy basis, treating interaction-induced (internal) and drive-induced (external) nonperturbative dressing on an equal footing. We subsequently investigate dissipation in two minimal driven open quantum systems---a harmonically driven two-level system and a harmonically driven coupled-two-level-system---each weakly coupled to a Markovian bath. Comparing the F-GME to a time-independent dressed-basis master equation, we show that even for a flat-bath spectral density and weak dissipation, the two approaches can yield qualitatively different steady-state populations and emission spectra. We resolve dissipation into drive-assisted sideband processes decaying via Floquet extended-space quasienergy channels, and show these channels can hybridize through nonsecular couplings into collective Floquet--Liouville modes governing observable spectral resonances. This analysis demonstrates that time-independent dissipative descriptions can incorrectly weight multiphoton Floquet transitions by collapsing quasienergy-resolved decay pathways into static energy gaps. The F-GME framework provides a systematic diagnostic for identifying regimes where Floquet-consistent dissipation is essential and clarifies the physical origin of discrepancies between commonly used master-equation approaches.
Understanding quantum coherence and proposing protection mechanisms has become one of the fundamental challenges in quantum physics research. We investigate a generic driven open quantum system, i.e., the driven spin-boson model, beyond the rotating-wave approximation. Although steady-state coherence vanishes in Floquet-Markov and Bloch-Redfield approaches, it becomes finite within a time-non-local master equation with a memory kernel. We analytically reveal that the steady-state coherence is associated with the overlap between the spectral densities associated with neighboring Floquet quasifrequencies. Motivated by this, we show that increasing temperature and introducing mixed transverse and longitudinal baths broadens the spectral density, thereby enhancing steady-state coherence. This is described by resonance fluorescence spectra, which exhibit clear spectral broadening and enhanced steady-state values. For a transverse dissipative coupling to the bath, three transition frequencies emerge in the Floquet basis, corresponding to the Mollow triplet. For weak resonant driving, these quasienergies become nearly degenerate, leading to closely spaced peaks in the resonance fluorescence spectrum, and the steady-state quantum coherence asymptotically approaches its maximum. For a longitudinal coupling to the bath, the quantum system exhibits a single transition frequency, thereby resulting in a complete suppression of the steady-state quantum coherence. We systematically investigate the influences of driving strength, frequency, temperature, and various dissipative baths on steady-state quantum coherence. These findings provide a foundational framework for efficiently engineering steady-state quantum coherence in nanoscale open quantum devices under optical field excitation.