Non-Markovian time evolution of an accelerated qubit

TL;DR

This paper introduces a non-Markovian approach to modeling the time evolution of an accelerated qubit interacting with a scalar field, revealing new insights into the thermalization process and the limitations of traditional Markovian assumptions.

Contribution

The authors develop a comprehensive non-Markovian framework for qubit evolution that applies to arbitrary trajectories and times, challenging the conventional Markovian approximation in quantum field interactions.

Findings

Non-Markovian effects are significant in the late-time thermalization of the qubit.

The late-time behavior of the detector accurately reflects the Unruh temperature.

Early-time transition rates do not show thermal behavior when non-Markovian effects are included.

Abstract

We present a new method for evaluating the response of a moving qubit detector interacting with a scalar field in Minkowski spacetime. We treat the detector as an open quantum system, but we do not invoke the Markov approximation. The evolution equations for the qubit density matrix are valid at all times, for all qubit trajectories and they incorporate non-Markovian effects. We analyze in detail the case of uniform acceleration, providing a detailed characterization of all regimes where non-Markovian effects are significant. We argue that the most stable characterization of acceleration temperature refers to the late time behavior of the detector, because interaction with the field vacuum brings the qubit to a thermal state at the Unruh temperature. In contrast, the early-time transition rate, that is invoked in most discussions of acceleration temperature, does not exhibit a thermal behavior when non-Markovian effects are taken into account. Finally, we note that the non-Markovian evolution derived here also applies to the mathematically equivalent problem of a static qubit interacting with a thermal field bath.