Towards the new generation of quantum sensors – ultracold atoms and NV centres

We simulate two different sensing platforms – the nitrogen-vacancy (NV) centre in diamond and Bose-Einstein condensates (BECs) in holographic ring traps – and consider how aspects such as sensitivity and speed can be characterised and optimised. For the case of NV centres, this thesis focuses on their application as high-resolution sensors of magnetic field and investigates optimising the speed of the sensing process as we track a changing magnetic field. Current methods for optimising tracking speed rely on machine learning calculations to reduce the number of measurements required. Our work adds to this speed improvement by reducing the computation time of these calculations via Gaussian approximation. This led to a reduction in computation time by factor 10 in all but the lowest coherence time case, where the more modest improvement in computation time is made up for by an increase in tracking accuracy compared to the original non-approximate method. In terms of the work with BECs, we perform both rotation and magnetic field sensing. To closer predict performance of experimental implementation, we consider the effect of shot noise in the presence of image pixelisation, as a camera would be in a physical set-up. After evaluating sensitivity, we found these to be competitive with state of the art quantum sensing alternatives. Additionally, we explore an innovative approach to engineer the wavefunction of the condensate to create a superposition state.