Unruh effect for detectors in superposition of accelerations

Luis C Barbado,Luca Apadula,Časlav Brukner,Esteban Castro-Ruiz

doi:10.1103/physrevd.102.045002

Abstract

The Unruh effect is the phenomenon that accelerated observers detect particles even when inertial observers experience the vacuum state. In particular, uniformly accelerated observers are predicted to measure thermal radiation that is proportional to the acceleration. Here we consider the Unruh effect for a detector that follows a quantum superposition of different accelerated trajectories in Minkowski spacetime. More precisely, we analyse the excitations of a pointlike multilevel particle detector coupled to a massless real scalar field and moving in the superposition of accelerated trajectories. We find that the state of the detector excitations is, in general, not a mere (convex) mixture of the thermal spectrum characteristics of the Unruh effect for each trajectory with well-defined acceleration separately. Rather, for certain trajectories and excitation levels, and upon the measurement of the trajectory state, the state of the detector excitations features in addition off-diagonal terms. The off-diagonal terms of these "superpositions of thermal states" are related to the distinguishability of the different possible states in which the field is left after its interaction with detector's internal degrees of the freedom.

Highlights

The Unruh effect is one of the cornerstone results of Quantum Field Theory in non-inertial frames or curved spacetime (QFT-CS), and the paradigmatic example of the frame-dependent notion of the particle content of a field
With this development we provide a first description of the Unruh effect in a particular family of Quantum Reference Frame (QRF), namely those which correspond to the superposition of accelerated trajectories which share the same Rindler wedge
We have studied the excitation of a particle detector following a quantum superposition of semiclassical trajectories with well-defined acceleration due to the Unruh effect

Summary

INTRODUCTION

The Unruh effect is one of the cornerstone results of Quantum Field Theory in non-inertial frames or curved spacetime (QFT-CS), and the paradigmatic example of the frame-dependent notion of the particle content of a field. We find that a critical condition for the states in which the field is left, corresponding to different trajectories and different excitation levels of the detector, not to be fully distinguishable is that the energy of the absorbed particle is the same as measured by any Rindler (accelerated) observer in the given Rindler wedge. This is in complete agreement with the fact that Minkowski vacuum state is a thermal bath as perceived by any accelerated observer, the local temperature perceived by different observers being different because of the non-trivial Tolman factor [27] of the metric in the Rindler wedge. In Appendix C we briefly consider the case in which the degrees of freedom of the detector (both the internal and the external) have a continuous spectrum

STATEMENT OF THE PROBLEM

State of the detector after the interaction

Physical interpretation

State of the internal energy levels

AN EXPLICIT EXAMPLE

FURTHER DISCUSSION