We study the dynamics of open quantum systems driven by an external time-periodic force. Combining Floquet theory and the time-convolutionless projection operator technique we derive a time-local quantum master equation which exactly takes into account the periodic driving, while treating the system-environment interaction within second order in the coupling strength without performing the Markov approximation. The resulting equation of motion for the reduced density matrix is called Floquet time-convolutionless master equation. Employing the example of the driven spin-boson system, we demonstrate that this master equation is capable of describing strong non-Markovian effects, while yielding the Floquet-Lindblad master equation in the Markovian limit. A characteristic feature of memory effects in such driven dissipative systems is the emergence of sharp peaks of the trace-distance based non-Markovianity measure as a function of the driving amplitude, which can be traced back to quasienergy crossings leading to almost decoherence-protected subspaces through a quasienergy-induced dissipative decoupling mechanism.
We study the dynamics of open quantum systems driven by an external time-periodic force. Combining Floquet theory and the time-convolutionless projection operator technique we derive a time-local quantum master equation which exactly takes into account the periodic driving, while treating the system-environment interaction within second order in the coupling strength without performing the Markov approximation. The resulting equation of motion for the reduced density matrix is called Floquet time-convolutionless master equation. Employing the example of the driven spin-boson system, we demonstrate that this master equation is capable of describing strong non-Markovian effects, while yielding the Floquet-Lindblad master equation in the Markovian limit. A characteristic feature of memory effects in such driven dissipative systems is the emergence of sharp peaks of the trace-distance based non-Markovianity measure as a function of the driving amplitude, which can be traced back to quasienergy crossings leading to almost decoherence-protected subspaces through a quasienergy-induced dissipative decoupling mechanism.
We study the emergence of quantum memory effects in a spin-boson system at finite temperature driven by an external time-periodic force. Quantifying memory effects by the trace-distance based measure for non-Markovianity and performing numerical simulations employing the hierarchical equations of motion approach, we find a pronounced peak structure when plotting the non-Markovianity measure as a function of the driving amplitude. This distinctive feature is interpreted using Floquet theory and the Floquet-Lindblad master equation, associating the peaks with the degeneracies of the quasienergy spectrum which lead to a strong enhancement of the relaxation times of the system. These results suggest strategies for the efficient control of non-Markovianity in open quantum systems by periodic driving.
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.
Being an exemplary model of open quantum system, the spin-boson model is widely employed in theoretical and experimental studies. Beyond the weak coupling limit, the spin-boson dynamics can be described by a time-nonlocal generalized master equation with a memory kernel accounting for the dissipative effects induced by the bosonic environment. When the spin is in addition modulated by an external time-periodic electromagnetic field, the interplay between dissipation and forcing provides a spectrum of nontrivial asymptotic states, especially so in the regime of nonlinear response. Here we implement the method for evaluating the dissipative Floquet dynamics of non-Markovian systems introduced in Magazzù et al. [Phys. Rev. A 96, 042103 (2017)2469-992610.1103/PhysRevA.96.042103] to obtain these nonequilibrium asymptotic states.
The dynamics of open quantum systems is commonly described by quantum master equations derived under the assumption of weak system-bath coupling and a separation of timescales between system and bath. When the system is additionally subjected to a periodic driving, the validity of the resulting Floquet master equations is further restricted to regimes of weak or high-frequency driving. Here, we benchmark a set of commonly used Floquet master equations for a model of two locally driven spins coupled to a shared Ohmic reservoir at finite temperature. We systematically probe the accuracy of the equations as a function of the driving parameters, thus identifying limits of their applicability. Dynamical maps predicted by each master equation are compared against numerically exact non-Markovian simulations, tracking the full relaxation dynamics. We find that the accuracy of each master equation closely reflects the assumptions underlying its derivation. For the Floquet-Lindblad equation, errors can be strongly amplified near resonances where the secular approximation breaks down, while approaches that avoid the secular approximation perform better and exhibit a more systematic dependence of the error on driving frequency and amplitude.
Time-periodic quantum systems are present all over science and technology. They have been successfully studied using Floquet theory, and a broad diversity of interesting phenomena such as coherent destruction of tunnelling, dynamical localization and creation of new phases of matter have been discovered. Furthermore, periodic driving has also been introduced as a tool for engineering novel quantum systems that have no static analogue. Besides these remarkable achievements for isolated systems, in reality, systems always interact with their surroundings. Taking the effect of the environment into account, time-periodic quantum systems have been mainly described using the Floquet-Markov approach, which consists in deriving a weak coupling master equation in the Floquet basis. In this thesis, we focus on how to overcome these standard approximations in the description of driven open quantum systems. We start by providing a general review on the topics of isolated driven systems, open quantum systems and the Floquet-Markov approach, before presenting the main results of this work. Under the effect of high-frequency driving, we provide an analytic solution to a large class of open quantum systems. Our method relies on discrete symmetries of the system-bath Hamiltonian and grants access to the time evolution operator of the full system, including bath degrees of freedom. The solution can be interpreted as the stroboscopic evolution of a family of observables under the influence of an effective static Hamiltonian. This provides a flexible simulation procedure of nontrivial Hamiltonians. The results are exemplified with the driven spin-boson model, where a coherent control of dissipation is observed. By a novel combination of Floquet theory, full counting statistics and a Markovian embedding strategy (reaction coordinate mapping), more intricate scenarios with additional driven system-environment interactions are addressed. Hereby, we can access the dynamics and thermodynamics of a periodically driven thermal machine. For the particular case where the working medium is a two-level system, we identify four different operating regimes, including a heat engine and a refrigerator. As the coupling strength is increased, their efficiency and coefficient of performance decrease and the refrigerator regime disappears. Notably, our model reproduces the setup of laser cooling of trapped ions in a specific parameter limit. Following the same combination of methods, we investigate electron pumping through a single quantum dot with periodically modulated energy and tunnelling amplitudes. In the high-frequency regime, the direction of the current can be controlled with the driving phase and a rectification effect that is exclusive to the non-Markovian character of the model is observed. In the low-frequency regime, we apply an additional transformation to view the model as three independent transport channels and observe that the coupling strength also controls the current direction. Studying charge fluctuations we validate that our model behaves as a single-electron source.
We present an approach for efficiently simulating strongly damped quantum systems subjected to periodic driving, employing a periodic matrix product operator representation of the influence functional. This representation enables the construction of a numerically exact Floquet propagator that captures the non-Markovian open system dynamics, thus providing a dissipative analogue to the Floquet Hamiltonian of driven isolated quantum systems. We apply this method to study the asymptotic heating of a reservoir in spin-boson models, characterizing the deviation from equilibrium conditions. Moreover, we show how a local driving of two qubits can be utilized to stabilize a transient entanglement buildup of the qubits originating from the interaction with a common environment. Our results make it possible to directly study both stationary and transient dynamics of strongly damped and driven quantum systems within a transparent theoretical and numerical framework.