Generalized theory of pseudomodes for exact descriptions of non-Markovian quantum processes

Abstract

We develop an exact framework to describe the non-Markovian dynamics of an open quantum system interacting with an environment modeled by a generalized spectral density function. The approach relies on mapping the initial system onto an auxiliary configuration, comprising the original open system coupled to a small number of discrete modes, which in turn are each coupled to an independent Markovian reservoir. Based on the connection between the discrete modes and the poles of the spectral density function, we show how expanding the system using the discrete modes allows for the full inclusion non-Markovian effects within an enlarged open system, whose dynamics is governed by an exact Lindblad master equation. Initially we apply this result to obtain a generalization of the pseudomode method [B. M. Garraway, Phys. Rev. A 55, 2290 (1997)] in cases where the spectral density function has a Lorentzian structure. For many other types of spectral density function, we extend our proof to show that an open system dynamics may be modeled physically using discrete modes which admit a non-Hermitian coupling to the system, and for such cases determine the equivalent master equation to no longer be of Lindblad form. For applications involving two discrete modes, we demonstrate how to convert between pathological and Lindblad forms of the master equation using the techniques of the pseudomode method.

Integral representation of finite temperature non-Markovian evolution of some RWA systems

“…But the main direction for further development is the generalization of these results for wider classes of RWA models. Also the possibility of dilation to the Gorini-Kossakowski-Sudarshan-Lindblad equation with a finite number of degrees of freedom for certain spectral densities is interesting due to the modern discussion of the pseudomode approach [25,26].…”

“…This dilation leads to the so-called pseudomode approach [16,17,18,19,20,21,22,14,15] which has been generalized to models without RWA [23,24] and non-zero temperature reservoirs [25] only recently. Also the generalization to other spectral densities was discussed in [26].…”

Non-perturbative effects in corrections to quantum master equation arising in Bogolubov-van Hove limit

“…Actually there is a well-developed theory of pseudomodes for such a spectral density, which was initially developed exactly for this model [57][58][59][60][61][62][63] but then was generalized to other models [87][88][89][90][91]. The spectral density is related to the bath correlation function G(t) = 1 2π e −iωt J(ω) (we follow [59] in the normalization constant choice).…”