Quantum regression theorem in the Unruh-DeWitt battery

TL;DR

This paper uses the quantum regression theorem to analytically study the correlation functions and emission spectrum of an accelerated quantum system acting as a relativistic quantum battery interacting with a scalar field.

Contribution

It introduces an analytical framework for the correlation functions and emission spectra of an Unruh-DeWitt detector in Rindler spacetime under the quantum regression theorem.

Findings

Acceleration enhances dissipation in the system.

Derived the spontaneous emission spectrum showing Lorentzian line shape.

Analyzed photon bunching effects in the context of Bose-Einstein statistics.

Abstract

In this paper, we employ the quantum regression theorem, a powerful tool in the study of open quantum systems, to analytically study the correlation functions of an Unruh-DeWitt detector, which is an uniformly accelerated two-level quantum system, absorbing charges from an external classical coherent pulse. The system can thus be viewed as a relativistic quantum battery that interacts with the environment of its perceived particles, namely, the quanta of a massless scalar field. By considering the relativistic battery moving in Rindler spacetime, under Born-Markov approximation, we derive the Gorini-Kossakowski-Sudarshan-Lindblad master equation governing the evolution of the system's reduced density matrix. Moreover, we perform the Fourier transformation of the Wightman functions and use exponential regularisation to compute the functional forms appearing in the master equation. Next, we derive the evolution equations for the the single-time expectation values of the system's operators. We not only solve these equations to find out the single time averages, but also employ the quantum regression theorem to determine the two-time correlation functions of first and second order. We analyse them to explain the phenomenon of spontaneous emission and show analytically how the acceleration can enhance the associated dissipation. Furthermore, we address a special form of second order correlation function relevant to the context of photon bunching arising in Bose-Einstein statistics. We analysed the results both analytically and graphically. Finally, we derive the spontaneous emission spectrum of the battery detector analytically, which in the long-time limit displays a well-defined Lorentzian line shape in the high frequency regime.