Abstract
We introduce a new dynamical picture, referred to as correlation picture,' which connects a correlated state to its uncorrelated counterpart. Using this picture allows us to derive an exact dynamical equation for a general open-system dynamics with system--environment correlations included. This exact dynamics is in the form of a Lindblad-like equation even in the presence of initial system-environment correlations. For explicit calculations, we also develop a weak-correlation expansion formalism that allows us to perform systematic perturbative approximations. This expansion provides approximate master equations which can feature advantages over existing weak-coupling techniques. As a special case, we derive a Markovian master equation, which is different from existing approaches. We compare our equations with corresponding standard weak-coupling equations by two examples, where our correlation picture formalism is more accurate, or at least as accurate as weak-coupling equations.
Highlights
The recent rise in high-fidelity quantum technological devices has necessitated detailed understanding of open quantum systems and how their environment influences their performance
To illustrate universality of the dynamical equation (9), even in the presence of initial system-bath correlations, we begin with a proof-of-principle example, the well-known, exactly solvable, Jaynes–Cummings model [41], and show that the dynamics of the two-level system is described by the universal Lindblad-like (ULL) equation even when the system is correlated with a bosonic mode
By using the Schrödinger equation of the total system, using a correlating transformation, and tracing over the environment degrees of freedom, we have found the dynamical equation of the subsystem without invoking any approximations
Summary
The recent rise in high-fidelity quantum technological devices has necessitated detailed understanding of open quantum systems and how their environment influences their performance. Despite previous attempts to prove the existence of universally valid time-local Lindblad-like master equations for general dynamics [15,16,17,18,19], a microscopic derivation that incorporates correlations, whether initial or instantaneous, within the dynamics has been elusive. We address these issues by introducing the correlation picture, a new technique through which we relate any correlated state of a composite system in the Schrödinger picture to an uncorrelated description of that system. We show that even the lowest order of the constructed ULL equation (ULL2) can outperform corresponding weak-coupling master equations, which shows that giving the principal role to correlations rather than coupling offers a strong alternative to existing weakcoupling techniques
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