Spatially Confined Superposed Unruh-DeWitt Detector Trajectories

Abstract

In the absence of a comprehensive theory of quantum gravity, operational approaches to relativistic quantum phenomena have become increasingly important to probe our understanding. Unruh-DeWitt detectors are a versatile and powerful tool in that arsenal, and have been used to analyze problems such as the Unruh effect and quantum information theory. This work aims to examine the effects of superpositions of trajectories on Unruh-DeWitt detectors, which has been of particular interest to studying relativistic quantum information, with a special focus on experimental applicability. This thesis investigates the response of a detector interacting with a massless scalar field in (3+1) Minkowski spacetime when placed in a superposition of trajectories. The trajectories are examined in four distinct geometric configurations, including both circularly revolving and static trajectories, for which the detector can be confined to a singular location or orbit. The response of a detector in superpositions of circular and static trajectories is compared to analogous incoherent mixed state systems, and interference effects from non-local interactions between the trajectories through the Wightman are revealed and discussed. An effective temperature measure for Unruh-DeWitt detectors is established and used to investigate the thermal properties of superposed detectors.

An experiment is proposed to test the response of a detector superposed at two distinct positions interacting with an analogue (2+1) massless scalar field. Using a beamsplitter allows for a single modulated laser source to pass through a Bose-Einstein condensate at two locations. We show that through a process of recombination of the beams and heterodyning, the response function of the detector can be obtained from the difference-photocurrent power spectral density. This is shown to explicitly include interference terms resulting from non-local interactions between the two superposed positions of the detector in the analogue field. We show that this can be done while operating beyond the standard quantum limit using squeezed light to obtain a greater signal-to-noise ratio.