Can we design a quantum sensor that can detect nearby electromagnetic fields in areas where the electromagnetic forces vanish? The objective of this project is to build a theoretical framework for
atomic sensors based on the Aharonov-Bohm (AB) and Aharonov-Casher (AC) effects [1]. These are geometric effects, where charged particles that traverse along a closed path surrounding the
field accumulate a phase proportional to the enclosed flux. This phase is typically detected interferometrically.

Initial experiments involved electron interferometers [2], but associated effects have been reported for both electric and magnetic dipoles and observed e.g. with neutrons and charge density waves within nano rings [3]. Neutral atoms have previously been used to demonstrate related effects [4], including the AC effect and the gravitational analogue to the AB, detecting electric fields with atoms in superpositions of different electronic states, and gravity with atoms in superpositions of motional states, respectively.

An attractive design for AB based magnetic field sensors could involve the use of different internal atomic states instead of separate external paths as the interferometric mechanism [5, 6]. Instead of enclosing the magnetic field within a closed motional path, here atoms in an internal superposition state would travel along a common path in the vicinity of the external magnetic field [7]. This could generate an effective closed loop, with the associated electric dipoles picking up different geometric phases, resulting in interference between the different internal states which could be read out optically. The PhD student will investigate detailed experimental designs including suitable atomic level structures and read-out mechanisms. They will analyse and optimize the experimental design using analytical and numerical methods based on time-dependent Schrödinger equations and Lindblad master equations, estimate sensitivity targets and consider relevant use cases in close collaboration with AWE.