Autonomous Stabilization of Floquet States Using Static Dissipation

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 static 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 quasienergy 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 non-classical states, such as high photon number Fock states, that can be prepared in the system cavity.

💡 Research Summary

Floquet engineering—using strong periodic drives to reshape the Hamiltonian of quantum systems—has become a cornerstone of modern atomic, condensed‑matter, and superconducting‑circuit research. Yet the very act of driving inevitably creates entropy: quasienergy states (the Floquet eigenstates) become mixed by native decay and dephasing, higher‑order processes allow absorption of drive photons into unwanted levels, and many‑body interactions spread energy throughout the system. Conventional autonomous cooling schemes (optical pumping, dark‑state engineering) fail in the Floquet context because laboratory‑frame decay simultaneously excites and de‑excites quasienergy levels, and engineered dissipators would need to track the time‑dependent Floquet basis.

Ritter et al. propose a remarkably simple solution: couple the driven system statically to an auxiliary mode that is lossy but not driven. In their concrete implementation the primary system is a strongly modulated transmon qubit (a two‑level spin in a rotating effective magnetic field) and the auxiliary is a microwave cavity with fixed resonance Δ and photon loss rate κ. The total Hamiltonian is a time‑dependent Jaynes–Cummings model, \