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Pseudomodes as an eective description of memory

Laura Mazzola, Sabrina Maniscalco, Jyrki Piilo, Kalle‐Antti Suominen, B. M. Garraway

Published Jan 1, 2009• 2 citations
OpenAlex

Abstract

Department of Physics and Astronomy, University of Sussex, Falmer, Brighton, BN1 9QH, United KingdomWe investigate the non-Markovian dynamics of two-state systems in structured reservoirs. Weestablish a connection between two theoretical quantum approaches, the pseudomodes [B. M. Gar-raway, Phys. Rev. A 55, 2290 (1997)] and the recently developed non-Markovian quantum jumpmethod [J. Piilo et al., Phys. Rev. Lett. 100, 180402 (2008)]. This connection provides a clearphysical picture of how the structured reservoir a ects the system dynamics, suggesting the role ofthe pseudomodes as e ective description of environmental memory.

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Department of Physics and Astronomy, University of Sussex, Falmer, Brighton, BN1 9QH, United KingdomWe investigate the non-Markovian dynamics of two-state systems in structured reservoirs. Weestablish a connection between two theoretical quantum approaches, the pseudomodes [B. M. Gar-raway, Phys. Rev. A 55, 2290 (1997)] and the recently developed non-Markovian quantum jumpmethod [J. Piilo et al., Phys. Rev. Lett. 100, 180402 (2008)]. This connection provides a clearphysical picture of how the structured reservoir a ects the system dynamics, suggesting the role ofthe pseudomodes as e ective description of environmental memory.
We investigate the non-Markovian dynamics of two-state systems in structured reservoirs. We establish a connection between two theoretical quantum approaches, the pseudomodes [B. M. Garraway, Phys. Rev. A 55, 2290 (1997)] and the recently developed non-Markovian quantum jump method [J. Piilo et al., Phys. Rev. Lett. 100, 180402 (2008)]. This connection provides a clear physical picture of how the structured reservoir affects the system dynamics, suggesting the role of the pseudomodes as effective description of environmental memory.
Abstract Following the recent paper (Teittinen et al 2019 New J. Phys. 21 123041), one can see that in general there is no simple relation between non-Markovianity and quantum speed limit. Here, we investigate the connection between quantum speed limit time and non-Markovianity of an atom in structured environments (reservoirs) whose dynamics is governed by an exact pseudomode master equation (Garraway 1997 Phys. Rev. A 55 2290). In particular, we find an inverse relation between them, which means that the non-Markovian feature of the quantum process leads to speedup of evolution. Thus, there is a link between quantum speedup and memory effects for specific cases of dynamical evolution. Our results might shed light on the relationship between the speedup of quantum evolution and the backflow of information from the environment to the system.
We develop an exact framework for describing 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.