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.
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.
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.
Floquet engineering, the control of a quantum system by means of time-periodic driving, allows to modify the properties of a system so that it is described by an approximate effective time-independent Hamiltonian. However, in the presence of interactions the stabilization of interesting many-body ground states of such effective Hamiltonians is possible only on a certain time scale, beyond which Floquet heating sets in, as it results from unwanted driving induced resonant excitation. Moreover, the preparation of the ground state of such Floquet engineered effective Hamiltonians usually has to be accomplished adiabatically, which is another source of heating, especially when a phase transition has to be passed in a large system. Here, we propose a general dissipative strategy for the preparation and stabilization of effective ground states that are protected by an energy gap, such as topologically ordered states. It is scalable and relies on coupling the driven system to a thermal bath, the properties of which are chosen so that it both suppresses Floquet heating and guides the system into a non-equilibrium steady state with a large occupation of the effective ground-state. The small residual occupations of effective excited states are non-thermal, reflecting the non-equilibrium nature of the scheme. We use the Floquet-Born-Markov master equation to verify the proposed strategy. In particular, we discuss the preparation of both a one-dimensional Mott insulator and a two-dimensional fractional Chern insulator in strongly driven Bose-Hubbard systems.
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 driving underlies Hamiltonian and gate engineering, and produces dynamical orders with no equilibrium counterpart. These phenomena are, however, transient in well-isolated systems. We show that statically coupled dissipative auxiliaries cool the system toward low-energy states of the Floquet-engineered Hamiltonian, stabilizing orders in the steady state. The excess energy density is controllably small at high drive frequency and weak coupling and is captured by rate theory based on Fermi's Golden Rule. We numerically confirm robust cooling in a Floquet-engineered transverse-field Ising chain in both phases, and demonstrate discrete time-crystalline order, with a period-doubled magnetization response, in the steady state of a long-range Ising chain. Our results provide a rare analytical handle on the steady states of driven dissipative systems.
Laser technology has developed and accelerated photo-induced nonequilibrium physics, from both the scientific and engineering viewpoints. Floquet engineering, i.e., controlling material properties and functionalities by time-periodic drives, is at the forefront of quantum physics of light-matter interaction. However, it is limited to ideal dissipationless systems. Extending Floquet engineering to various materials requires understanding of the quantum states emerging in a balance of the periodic drive and energy dissipation. Here, we derive a general description for nonequilibrium steady states (NESSs) in periodically driven dissipative systems by focusing on systems under high-frequency drive and time-independent Lindblad-type dissipation. Our formula correctly describes the time average, fluctuation, and symmetry properties of the NESS, and can be computed efficiently in numerical calculations. This approach will play fundamental roles in Floquet engineering in a broad class of dissipative quantum systems from atoms and molecules to mesoscopic systems, and condensed matter.
Autonomous stabilization of many-body quantum states requires a mechanism that continuously removes stabilizer violations without relying on measurement and feedback. Here we develop a Floquet-Lindblad framework for scalable stabilizer pumping in neutral Rydberg atom arrays. Periodically modulated Rydberg excitation selectively couples the negative-eigenvalue sector of a prescribed stabilizer to auxiliary Rydberg states, while engineered dissipation irreversibly transfers the population into the corresponding positive-eigenvalue sector and leaves the target stabilizer manifold dark. This establishes a modular pumping primitive that can be composed to autonomously stabilize general many-body stabilizer manifolds, rather than merely prepare a specific entangled state. The combination of Floquet-selective excitation and fast engineered dissipation accelerates convergence, while transient single-Rydberg excitation and suppressed real multi-Rydberg occupation reduce sensitivity to Rydberg-state loss, blackbody-radiation-induced leakage, and spatial fluctuations. We demonstrate the framework through Bell and multiqubit graph states, including parallel stabilizer pumping that reduces the convergence time for the simulated multiqubit systems. The same dissipative attraction also enables purification of imperfect resource states. These results establish Floquet-engineered stabilizer pumping as a scalable route toward autonomous quantum-state stabilization and protected entanglement generation in neutral-atom platforms.