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.
Highlights
The theory of open quantum systems, which concerns the interaction between a quantum system of interest and a large macroscopic reservoir or heat bath [1,2], plays a fundamental role in several applications of quantum physics, ranging from quantum information [3], quantum technologies, and decoherence [4,5], through to quantum optics [6], condensed matter [7], and quantum thermodynamics [8]
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
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
Summary
The theory of open quantum systems, which concerns the interaction between a quantum system of interest and a large macroscopic reservoir or heat bath [1,2], plays a fundamental role in several applications of quantum physics, ranging from quantum information [3], quantum technologies, and decoherence [4,5], through to quantum optics [6], condensed matter [7], and quantum thermodynamics [8]. By expanding the system over the pseudomodes, one can derive a Lindblad master equation describing the dynamics induced by the non-Markovian interaction between the pseudomodes and two-level system, in addition to the coupling of the pseudomodes to an external Markovian environment While this method is exact, its application is currently restricted to regimes where only one excitation is initially present in the system, as well as to interactions valid within the rotating wave approximation. In this paper we extend this treatment to instances where the exact dynamics of the enlarged system is described by a non-Lindblad form of master equation with a non-Hermitian interaction Hamiltonian, as well as to physical environments modeled by a generalized spectral density function To achieve this we explicitly generalize the proof given in Ref.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
