Sambe approach to Floquet-Lindblad open quantum systems
Abstract:
We study open quantum systems described by a time-periodic Lindblad master equation. When the system is closed, the stroboscopic dynamics can always be described by an effective time-independent Floquet Hamiltonian; this idea is the basis for Floquet engineering. However, in the presence of dissipation, the existence of an effective time-independent Floquet Lindbladian is not guaranteed due to the non-unitary nature of the evolution. Using Floquet theory, we construct a well-defined time-independent Floquet Lindbladian acting in an extended Liouville space. The original time-dependent problem is therefore mapped to an equivalent time-independent and non-Hermitian eigenvalue problem. For harmonic driving, we introduce a matrix continued fraction method to nonperturbatively resum multiphoton processes and construct an effective Floquet Lindbladian acting only on the physical Liouville space. As an application, we consider a dissipating two-level system driven by a linearly polarized field for which we compute the spectrum of resonance fluorescence beyond the rotating-wave approximation. Our method offers a natural approach to Floquet-Lindblad problems beyond the perturbative regime and offers a controlled way to derive an effective Floquet Lindbladian. It can find natural applications in driven mesoscopic systems, quantum thermodynamics and driven-dissipative many-body systems.
Reference: Andriani Keliri and Marco Schirò, arXiv:2606.09727 (2026).
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