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.