Gravitational wave signals in an Unruh-DeWitt detector

TL;DR

This paper studies how gravitational waves affect a quantum Unruh-DeWitt detector, revealing a purely quantum effect where the detector's transition rate is non-analytic in the gravitational wave strain, challenging classical approximations.

Contribution

It generalizes the scalar propagator for gravitational waves and uncovers a non-analytic quantum response of the detector to gravitational wave backgrounds.

Findings

Detector's transition rate is exponentially suppressed with energy and scalar mass.

Quantum interference causes a non-analytic dependence on gravitational wave strain.

Gravitational waves induce a continuum of energy transitions in the detector.

Abstract

We firstly generalize the massive scalar propagator for planar gravitational waves propagating on Minkowski space obtained recently in Ref. [1]. We then use this propagator to study the response of a freely falling Unruh-DeWitt detector to a gravitational wave background. We find that a freely falling detector completely cancels the effect of the deformation of the invariant distance induced by the gravitational waves, such that the only effect comes from an increased average size of scalar field vacuum fluctuations, the origin of which can be traced back to the change of the surface in which the gravitational waves fluctuate. The effect originates from the quantum interference between propagation on off-shell detector's trajectories which probe different spatial gravitational potential induced by the gravitational backreaction from gravitational waves, and it is therefore purely quantum. When resummed over classical graviton insertions, gravitational waves generate cuts on the imaginary axis of the complex $\Delta \tau$-plane (where $\Delta \tau = \tau-\tau'$ denotes the difference of proper times), and the discontinuity across these cuts is responsible for a continuum of energy transitions induced in the Unruh-DeWitt detector. Not surprisingly, we find that the detector's transition rate is exponentially suppressed with increasing energy and the mass of the scalar field. What is surprising, however, is that the transition rate is a non-analytic function of the gravitational field strain. This means that, no matter how small is the gravitational field amplitude, expanding in powers of the gravitational field strain cannot approximate well the detector's transition rate.