High-frequency expansions for time-periodic Lindblad generators

Abstract

Floquet engineering of isolated systems is often based on the concept of the effective time-independent Floquet Hamiltonian, which describes the stroboscopic evolution of a periodically driven quantum system in steps of the driving period and which is routinely obtained analytically using high-frequency expansions. The generalization of these concepts to open quantum systems described by a Markovian master equation of Lindblad type turns out to be non-trivial: On the one hand, already for a two-level system two different phases can be distinguished, where the effective time-independent Floquet generator (describing the stroboscopic evolution) is either again Markovian and of Lindblad type or not. On the other hand, even though in the high-frequency regime a Lindbladian Floquet generator (Floquet Linbladian) is numerically found to exist, this behaviour is, curiously, not correctly reproduced within analytical high-frequency expansions. Here, we demonstrate that a proper Floquet Lindbladian can still be obtained from a high-frequency expansion, when treating the problem in a suitably chosen rotating frame. Within this approach, we can then also describe the transition to a phase at lower driving frequencies, where no Floquet Lindbladian exists, and show that the emerging non-Markovianity of the Floquet generator can entirely be attributed to the micromotion of the open driven system.

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• Quantum thermodynamics with fast driving and strong coupling via the mesoscopic leads approach
• Cavity-based reservoir engineering for Floquet-engineered superconducting circuits
• Floquet-engineered nonlinearities and controllable pair-hopping processes: From optical Kerr cavities to correlated quantum matter
• Floquet engineering of optical nonlinearities: a quantum many-body approach
• Fitting quantum noise models to tomography data
• Periodically Driven Open Quantum Systems: Spectral Properties and Non-Equilibrium Steady States
• Floquet-heating-induced Bose condensation in a scar-like mode of an open driven optical-lattice system
• Flow-equation approach to quantum systems driven by an amplitude-modulated time-periodic force
• Efficient Lindblad synthesis for noise model construction
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• Floquet dynamics of Rabi model beyond the counterrotating hybridized rotating wave method
• Floquet dynamical chiral spin liquid at finite frequency
• Coherent and Dissipative Spin Torques in Quantum Dots: A Unified Framework for Quantum Spin Dynamics