Optimal Superpositions for Particle Detection via Quantum Phase

TL;DR

This paper investigates the optimal size of quantum superpositions for detecting incident particles from specific directions, revealing a link between superposition size, scattering, and particle wavelength in quantum sensing.

Contribution

It introduces the concept of an optimal superposition size for particle detection, considering scattering effects and environmental anisotropy, which was not addressed in prior work.

Findings

Identifies an optimal superposition size for directional particle detection.

Shows the optimal size depends on the wavelength of the scatterer.

Reveals a novel behavior in the system's density matrix related to environment anisotropy.

Abstract

Exploiting quantum mechanics for sensing offers unprecedented possibilities. State of the art proposals for novel quantum sensors often rely on the creation of large superpositions and generally detect a field. However, what is the optimal superposition size for detecting an incident particle (or an incident stream of particles) from a specific direction? This question is nontrivial as, in general, this incident particle will scatter off with varied momenta, imparting varied recoils to the sensor, resulting in decoherence rather than a well defined measurable phase. By considering scattering interactions of directional particulate environments with a system in a quantum superposition, we find that there is an "optimal superposition" size for measuring incoming particles via a relative phase. As a consequence of the anisotropy of the environment, we observe a novel feature in the limiting behaviour of the real and imaginary parts of the system's density matrix, linking the optimality of the superposition size to the wavelength of the scatterer.