Unruh-deWitt detectors in quantum superpositions of trajectories

Unruh-deWitt detectors have been utilised widely as probes for quantum particles, entanglement and spacetime curvature. Here, we extend the standard treatment of an Unruh-deWitt detector interacting with a massless, scalar field to include the detector travelling in a quantum superposition of classical trajectories. We derive perturbative expressions for the final state of the detector, and show that it depends on field correlation functions evaluated locally along the individual trajectories, as well as non-locally between the superposed trajectories. By applying our general approach to a detector travelling in a superposition of two uniformly accelerated trajectories, including those with equal and differing proper accelerations, we discover novel interference effects in the emission and absorption spectra. These effects can be traced to causal relations between the superposed trajectories. Finally, we show that in general, such a detector does not thermalise even if the superposed paths would individually yield the same thermal state.