Abstract
A novel method based on spectral Green functions is presented for the simulation of driven open quantum dynamics that can be described by the Lindblad master equation in Liouville density operator space. The method extends the Hilbert space formalism and provides simple algebraic connections between the driven and non-driven dynamics in the spectral frequency domain. The formalism shows remarkable analogies to the use of Green functions in quantum field theory such as the elementary excitation energies and the Dyson self-energy equation. To demonstrate its potential, we apply the novel method to a coherently driven dissipative ensemble of 2-level systems comprising a single "active" subsystem interacting with $N$ "passive" subsystems -- a generic model with important applications in quantum optics and dynamic nuclear polarization. The novel method dramatically reduces computational cost compared with simulations based on solving the full master equation, thus making it possible to study and optimize many-body correlated states in the physically realistic limit of an arbitrarily large $N$.
Highlights
INTRODUCTIONOpen quantum dynamics takes into account the environment (outer degrees of freedom) and so more accurately describes real physical phenomena compared with closed quantum dynamics based entirely on the energy operator (inner Hamiltonian)
Open quantum dynamics takes into account the environment and so more accurately describes real physical phenomena compared with closed quantum dynamics based entirely on the energy operator
The Lindblad master equation approach can be used that retains the positivity of the density operator and introduces the environmental effects through Markovian quantum jump operators that enter the dissipator in a simple algebraic way [1,2,3,4,5,6]
Summary
Open quantum dynamics takes into account the environment (outer degrees of freedom) and so more accurately describes real physical phenomena compared with closed quantum dynamics based entirely on the energy operator (inner Hamiltonian). For the description of collective phenomena in large-scale closed quantum systems at thermal equilibrium, a method involving the use of Green’s functions was developed that statistical physics adopted from quantum field theory [7,8,9] This method is based on the approximate calculation of correlations between dynamic operators that leads to selfconsistent equations for the observables. We propose an extension of the nonequilibrium spectral approach to the important class of driven Markovian open quantum dynamics in the Liouville space of the density operator To this end, we show that the Green’s function for an inhomogeneous spectral problem can be formulated in terms of both Hamiltonian and dissipative parts of the Lindblad master equation. This enhances possibilities in simulations of many-body driven open quantum dynamics, including the spectral response to the driving and the fast search for the optimal parameter regions
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