Abstract
Nonequilibrium steady states (NESSs) in periodically driven dissipative quantum systems are vital in Floquet engineering. We develop a general theory for high-frequency drives with Lindblad-type dissipation to characterize and analyze NESSs. This theory is based on the high-frequency (HF) expansion with linear algebraic numerics and without numerically solving the time evolution. Using this theory, we show that NESSs can deviate from the Floquet-Gibbs state depending on the dissipation type. We also show the validity and usefulness of the HF-expansion approach in concrete models for a diamond nitrogen-vacancy (NV) center, a kicked open XY spin chain with topological phase transition under boundary dissipation, and the Heisenberg spin chain in a circularly-polarized magnetic field under bulk dissipation. In particular, for the isotropic Heisenberg chain, we propose the dissipation-assisted terahertz (THz) inverse Faraday effect in quantum magnets. Our theoretical framework applies to various time-periodic Lindblad equations that are currently under active research.
Highlights
Throughout this section, we focus on a widely-accepted special class of Floquet-Lindblad equation (FLE): the quantum master equation obtained by the rotating wave approximation (RWA) [41, 85]
We have theoretically studied the nonequilibrium steady states (NESSs) in the time-periodic quantum master equation of Lindblad form
One important consequence is that, the effective Liouvillian is not necessarily of Lindblad form (Lindbladian), it is still useful to analyze the NESSs. This is mainly because the effective Liouvillian is trace-preserving (Lemma 1) and the NESS is guaranteed to exist at each order of the HF expansion (Theorem 1)
Summary
Driven quantum systems have seen a resurgence of interest motivated by laser technology advancement and theoretical developments [1,2,3,4,5]. We derive such FLEs with a slight generalization of previous studies in that one allows the Floquet quasienergies to be degenerate, and we reveal the conditions for the NESS being approximated by the Floquet-Gibbs state. Since we have shown the existence of the zero eigenvalue, it means that the maximum of the eigenvalues real parts is zero This property is important to obtain sensible time evolution since if Leff had an eigenvalues with a positive real part (and VF had one with absolute value greater than 1), the density operator would blow up in many cycles of evolution. We leave the general proof of the nonpositivity as an open problem and assume the nonpositivity throughout this work
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