Can a pure state remain pure in the Unruh effect?

TL;DR

This paper investigates conditions under which two entangled atoms can avoid thermalization due to the Unruh effect, revealing a critical acceleration limit that preserves quantum purity and induces a phase transition.

Contribution

It demonstrates the existence of a critical acceleration limit for two atoms where quantum purity is maintained, introducing the concept of a decoherence-free subspace in this context.

Findings

A critical acceleration exists below which the initial quantum state remains pure.

A symmetry of the Lindbladian operator leads to a decoherence-free subspace.

A first-order phase transition occurs from localized to thermal states beyond the critical acceleration.

Abstract

A uniformly accelerated detector in an inertial vacuum undergoes an unavoidable dissipation, and the final steady-state becomes thermal. However, to attain such a mixed state, there is no bound for the acceleration of the single atomic detector. Here we show that the scenario is entirely different for two atoms with the same energy levels. There exists a critical limit of the acceleration for two atomic detectors, below which the purity of a particular initial state can be preserved. We observe that the generator of the dissipative dynamics (Lindbladian) is invariant under a weak symmetry transformation at this limit. Hence one of the eigenstates of the symmetry operator is unchanged during the evolution. This kind of state is called a quantum dark state, which is essentially a decoherence-free subspace. As a consequence, the system becomes localized, and it can skip the Unruh thermalization. Beyond the critical limit, the symmetry is explicitly broken. Therefore our results suggest that the system goes through a first-order dissipative phase transition from a localized to a thermal phase.