Role of initial system-environment correlations: A master equation approach

Abstract

In order to achieve practical implementations of emerging quantum technologies, it is important to have a firm understanding of the dynamics of realistic quantum open systems. Master equations provide a widely used tool in this regard. In this work, we first construct a master equation, valid for weak system-environment coupling, which explicitly takes into account the impact of preparing an initial system state from an equilibrium system-environment state that has system-environment correlations. We then investigate the role of initial system-environment correlations using this master equation for a system consisting of many two-level atoms interacting with a common environment. We show that, in general, due to the initial system-environment correlations before a state preparation, the quantum state of the system can evolve at a faster time-scale. Moreover, we also consider different initial state preparations, and demonstrate that the influence of state preparations depends on the initial states prepared. Our results can be of interest to many topics based on quantum open systems where system-environment correlation effects have been neglected before.

Dynamics of non-Markovian open quantum systems

“…This type of initial conditions was discussed by Grabert et al (1988) for the case of a quantum Brownian particle, when considering the state prepared by measuring a dynamical variable such as the position of the particle q. More recently, Chaudhry and Gong (2013) derived a weak coupling master equation from the initial state obtained after a single measure that projects the system to the state |ψ 0 . In such a case, the initial state can be written as…”

Initial system-environment correlations via the transfer-tensor method

“…However, numerous questions crucially require to account for initial correlations between the open system of interest and its environment. Apart from witnessing or certifying their existence [3][4][5][6][7][8], they find very concrete applications such as the correct simulation of emission spectra of molecular systems [9][10][11] or their thermodynamic effect for the extractable work of thermal machines [12,13]. Although it has recently been pointed out that correlations may play a relevant role already in the weak system-environment coupling regime [5], it is in situations of strong coupling to a non-Markovian environment where initial correlation effects are expected to be most significant.…”

The quantum Zeno and anti-Zeno effects: from weak to strong system-environment coupling

“…In order to compute s(τ ), we need to write down the initial state of the system. The combined initial state of the system and the environment cannot be written as a product state because of strong system environment correlations [25,56,57]. The initial state of the system that we consider is |↑ , with σ z |↑ = |↑ , which is the state usually used in the study of the population decay model [25,30,31].…”