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International Journal of Quantum Information

Enhancement of non-Markovianity by interference of two reservoirs

X. Y. Zhang, X. L. Huang, X. X. Yi

Published Sep 1, 2015• 1 citation
Publisher

Abstract

We study the effect of the interference between two independent non-Markovian reservoirs on the non-Markovianity of a two-level system. We find that the interference can enhance the non-Markovianity of the system. The additive master equation (ME) is invalid even if only one of the two reservoirs is non-Markovian, while it is a good approximation when all reservoirs are Markovian. We also derive the two states uniqueness for a two-level system coupled to structured reservoirs which maximize the measure of non-Markovianity defined by Breuer et al. [Phys. Rev. Lett. 103 (2009) 210401].

DOI
10.1142/s0219749915500483

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We study the effect of the interference between two independent non-Markovian reservoirs on the non-Markovianity of a two-level system. We find that the interference can enhance the non-Markovianity of the system. The additive master equation (ME) is invalid even if only one of the two reservoirs is non-Markovian, while it is a good approximation when all reservoirs are Markovian. We also derive the two states uniqueness for a two-level system coupled to structured reservoirs which maximize the measure of non-Markovianity defined by Breuer et al. [Phys. Rev. Lett. 103 (2009) 210401].
By use of the measure, the backflow of information presented recently, we study the non-Markovianity of the dynamics for a two-level system interacting with a zero-temperature structured environment via amplitude-phase coupling. In the limit of weak coupling between the system and its reservoir, the time-local non-Markovian master equation for the reduced state of the system is derived. Under the secular approximation, the exact analytic solution is obtained. Numerical simulations show that the amplitude and phase dampings can produce destructive interference to the backflow of information, leading to the weaker non-Markovianity of the compound dynamics compared with the dynamics of a single amplitude or phase damping model. We also study the characteristics of the initial-state pairs that maximize the backflow of information.
In stochastic thermodynamics, it is commonly assumed that for a system coupled to multiple thermal reservoirs, the transition rates between two energy levels are additive across baths. In this work, we first demonstrate through an explicit construction of two subsystems-that are parts of a single composite system, each coupled to a distinct thermal reservoir-that while each subsystem individually evolves Markovianly, their joint evolution is inherently non-Markovian. We then present a general algebraic argument showing that, even if one assumes a Markovian description with additive transition rates, the steady-state condition imposed by the master equation leads to an inconsistency. The analysis identifies the precise structural limitation that arises in describing systems simultaneously interacting with multiple baths within a Markovian framework.
When a quantum system interacts with multiple reservoirs, the environmental effects are usually treated in an additive manner. We show that this assumption breaks down for non-Markovian environments that have finite memory times. Specifically, we demonstrate that quantum interferences between independent environments can qualitatively modify the dynamics of the physical system. We illustrate this effect with a two-level system coupled to two structured photonic reservoirs, discuss its origin using a nonequilibrium diagrammatic technique, and show an example when the application of this interference can result in an improved dark state preparation in a $\ensuremath{\Lambda}$ system.
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.
We study the non-Markovian quantum interference phenomenon of a multi-state atomic system coupled to a bosonic dissipative environment by using the exact master equations derived in this paper. Two examples involving four-level systems with or without external control fields are investigated. Our results show that non-Markovian master equations are capable of exhibiting quantum interference phenomena in a temporal domain that has not fully explored before. In particular, we show that the environmental memory is instrumental in the onset of non-Markovian quantum interference pattern in different time scales.