Floquet-Markov description of the parametrically driven, dissipative harmonic quantum oscillator

How to understand the order of Floquet stationary states in the presence of external bath coupling and their statistical mechanics is challenging; the answers are important for preparations and control of those Floquet states. Here, we propose a scheme to classify the statistical distribution of Floquet states for time-periodic systems which couple to an external heat bath. If an effective Hamiltonian and a system-bath coupling operator, which are all time-independent, can be...

This work explores a fundamental dynamical structure for a wide range of many-body quantum systems under periodic driving. Generically, in the thermodynamic limit, such systems are known to heat up to infinite temperature states after infinite-time evolution, irrespective of dynamical details. In the present study, instead of considering infinitely long-time scale, we aim to provide a framework to understand the long but finite time behavior, namely the transient dynamics. In...

We present a short derivation and discussion of the master equation for an open quantum system weakly coupled to a heat bath and then its generalization to the case of with periodic external driving based on the Floquet theory. Further, a single heat bath is replaced by several ones. We present also the definition of heat currents which satisfies the second law of thermodynamics and apply the general results to a simple model of periodically modulated qubit.

By directly using the probability formulas of quantum trajectories, we construct an auxiliary open quantum system for a periodically driven open quantum system whose dynamics is governed by the Floquet quantum master equation. This auxiliary system can generate a quantum trajectory ensemble that is consistent with the canonical quantum trajectory ensemble. We find that, at a long time limit, though the Lindblad operators are modified, the coherent dynamics of the auxiliary sy...

The dynamics of qubits coupled to a harmonic oscillator with time-periodic coupling is investigated in the framework of Floquet theory. This system can be used to model nonadiabatic phenomena that require a periodic modulation of the qubit/oscillator coupling. The case of a single qubit coupled to a resonator populated with $n= 0,1$ photons is explicitly treated. The time-dependent Schr\"{o}dinger equation describing the system's dynamics is solved within the Floquet formalis...

We study probability distribution of a steady state of a periodically driven system coupled to a thermal bath by using a quantum master equation in the weak coupling limit. It is proved that, even when the external field is strong, the probability distribution is independent of the detailed nature of the thermal bath under the following conditions: (i) the Hamiltonian of the relevant system is bounded and the period of the driving field is short, (ii) the Hamiltonians for the...

The Lindblad equation, which describes Markovian quantum dynamics under dissipation, is usually derived under the weak system-bath coupling assumption. Strong system-bath coupling often leads to non-Markov evolution. The singular-coupling limit is known as an exception: it yields a Lindblad equation with an arbitrary strength of dissipation. However, the singular-coupling limit requires high-temperature limit of the bath, and hence the system ends up in a trivial infinite-tem...

We investigate signatures of non-Markovianity in the dynamics of a periodically-driven qubit coupled to a dissipative bosonic environment. We propagate the dynamics of the reduced density matrix of the qubit by integrating the numerically exact hierarchical equations of motion. Non-Markovian features are quantified by comparing the prediction from diverse and complementary approaches to quantum dissipation. In particular, we analyze the distinguishability of quantum states, t...

At the moment, the most efficient method to compute the state of a periodically driven quantum system is using Floquet theory and the Floquet eigenbasis. The wide application of this basis set method is limited by: a lack of unique ordering of the Floquet eigenfunctions, an ambiguity in their definition at resonance, and an instability against infinitesimal perturbation at resonance. We address these problems by redefining the eigenbasis using a revised definition of the aver...

We study the dissipative quantum Duffing oscillator in the deep quantum regime with two different approaches: The first is based on the exact Floquet states of the linear oscillator and the nonlinearity is treated perturbatively. It well describes the nonlinear oscillator dynamics away from resonance. The second, in contrast, is applicable at and in the vicinity of a N-photon resonance and it exploits quasi-degenerate perturbation theory for the nonlinear oscillator in Floque...