Non-Gaussian dynamics of quantum fluctuations and mean-field limit in open quantum central spin systems

TL;DR

This paper derives exact results for open quantum central spin systems, revealing how different interaction scalings lead to either non-Gaussian quantum fluctuations or mean-field dynamics, enhancing understanding of their complex behavior.

Contribution

It provides a comprehensive theory connecting interaction scaling with emergent dynamics, including non-Gaussian correlations and mean-field regimes, in open quantum central spin systems.

Findings

At inverse square root scaling, the system behaves as an open quantum Jaynes-Cummings model.

Non-Gaussian correlations are generated and persist at stationarity.

At inverse bath size scaling, the dynamics are of mean-field type.

Abstract

Central spin systems, in which a {\it central} spin is singled out and interacts nonlocally with several {\it bath} spins, are paradigmatic models for nitrogen-vacancy centers and quantum dots. They show complex emergent dynamics and stationary phenomena which, despite the collective nature of their interaction, are still largely not understood. Here, we derive exact results on the emergent behavior of open quantum central spin systems. The latter crucially depends on the scaling of the interaction strength with the bath size. For scalings with the inverse square root of the bath size (typical of one-to-many interactions), the system behaves, in the thermodynamic limit, as an open quantum Jaynes-Cummings model, whose bosonic mode encodes the quantum fluctuations of the bath spins. In this case, non-Gaussian correlations are dynamically generated and persist at stationarity. For scalings with the inverse bath size, the emergent dynamics is instead of mean-field type. Our work provides a fundamental understanding of the different dynamical regimes of central spin systems and a simple theory for efficiently exploring their nonequilibrium behavior. Our findings may become relevant for developing fully quantum descriptions of many-body solid-state devices and their applications.