Memory Effects and Entanglement Dynamics of Finite time Acceleration

TL;DR

This paper investigates how finite-duration acceleration affects entanglement and memory effects in Unruh-DeWitt detectors, revealing that correlations recover after acceleration and that memory influences Fisher information but not negativity.

Contribution

It introduces a smooth finite-time acceleration trajectory and analyzes its impact on detector dynamics, entanglement, and memory effects, extending understanding of relativistic quantum information.

Findings

Memory effects are present due to finite acceleration duration.

Total correlations and entanglement return to initial values after acceleration.

Memory effects do not significantly influence negativity or mutual information.

Abstract

We construct a smooth trajectory in Minkowski spacetime that is inertial in the asymptotic past and future but undergoes approximately uniform acceleration for a finite duration. In a suitable limit, this trajectory reduces to the standard Rindler trajectory, reproducing the expected Bogoliubov transformations and results consistent with the thermal time hypothesis. We analyze the behavior of an Unruh-DeWitt (UDW) detector following such a trajectory and explore the dependence of complete positivity (CP) divisibility on the detector's frequency, acceleration, and the duration of acceleration. Notably, we find that the detector exhibits a memory effect due to the finite duration of acceleration, which is also quantified by the Fisher information. We further examine two UDW detectors along various trajectory combinations and show that, unlike the transition rate, both the total correlation and the entanglement harvested return smoothly to their initial values after the acceleration/deceleration phase. These correlation measures behave similarly in both accelerating and decelerating segments. Interestingly, we do not observe any measurable effect of the memory effect on negativity or mutual information. We also discuss the physical significance of the sign of the flux of acceleration-induced radiation.