  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.
