Testing Superpositions of Detector Trajectories

TL;DR

This paper proposes an experiment to test the response of a particle detector in a superposition of locations interacting with a quantum field, utilizing laser beams, Bose-Einstein condensates, and heterodyne detection.

Contribution

It introduces a feasible experimental setup to observe superpositions of detector trajectories interacting with a relativistic quantum field.

Findings

Response function appears in the difference photocurrent power spectrum.

Estimated SNR of approximately 10 using squeezed light.

Demonstrates the potential to operate beyond the standard quantum limit.

Abstract

We propose a realizable experiment to test the response of a particle detector prepared in a superposition of locations interacting with a relativistic quantum field. Using a beamsplitter to prepare two superposed branches of a modulated laser probe, these branches are directed to intersect a pancake-shaped Bose-Einstein condensate at two separate locations. The branches are then recombined with another beamsplitter. Heterodyning one of the outputs, the response function corresponding to an Unruh-deWitt detector in a superposition of locations interacting with a (2+1)-dimensional massless scalar field is shown to appear in the difference photocurrent power spectrum. Operating beyond the standard quantum limit using squeezed light, we estimate the signal-to-noise ratio $SNR\gtrsim 10$ for extracting the response function over a broad set of baseband frequencies.