Uniformly accelerated quantum counting detector in Minkowski and Fulling vacuum states

TL;DR

This paper analyzes the response of a uniformly accelerated quantum detector interacting with a scalar field in various states, including Minkowski vacuum, revealing how acceleration influences detection probabilities and interpretations.

Contribution

It provides a detailed evaluation of the transition probability rate for an accelerated detector in different field states, including the Minkowski vacuum, using Glauber photodetection theory.

Findings

Accelerated detector excitation rates are equal in Minkowski vacuum and thermal states.

Transition probability rate in the far future mimics that of a detector in a thermal environment.

Inertial and accelerated observer perspectives are compared and discussed.

Abstract

In this work we discuss the process of measurements by a detector in an uniformly accelerated rectilinear motion, interacting linearly with a massive scalar field. The detector model for field quanta is a point-like system with a ground state and a continuum of unbounded states. We employ the Glauber theory of photodetection. In an uniformly accelerated reference frame, the detector, interacting with the field prepared in an arbitrary state of the Rindler Fock space, is excited only by absorption processes. For the uniformly accelerated detector prepared in the ground state, we evaluate the transition probability rate in three important situations. In the first one the field is prepared in an arbitrary state of $n$-Rindler quanta, then we consider a thermal Rindler state at a given temperature $\beta^{-1}$, and finally the case in which the state of the field is taken to be the Minkowski vacuum. The well-known result that the latter excitation rates are equal is recovered. Accelerated or inertial observer interpretations of the measurements performed by the accelerated detector is presented. Finally, we investigate the behaviour of the detector in a frame which is inertial in the remote past but in the far future becomes uniformly accelerated. For the massless case, we obtain that the transition probability rate of the detector in the far future is tantamount to the analogous quantity for the detector at rest in a non-inertial reference frame interacting with the field prepared in an usual thermal state.