Balanced gain and loss in an open quantum system results in PT symmetry which can lead to real eigenvalues and stable dynamics, even in a non-hermitian setting. It is generally believed that operating a PT symmetric device around an exceptional point will lead to enhanced sensitivity. To date, much of the work done has been in photonic systems, where it is experimentally more realisable to achieve the balanced gain and loss required for this PT symmetry. There has been less done towards exploring the role of PT symmetry in sensitivity in atomic matterwave devices. Moreover, the dynamics that results from the presence of PT symmetry in a many body atomic system is fundamentally very interesting and there is still much to discover within. This project will take steps to explore PT symmetry in an atomic matterwave gyroscope, and question whether or not this symmetry will lead to an increase in sensitivity to rotations. The student will investigate a toy model which approximately describes a matterwave gyroscope, with the addition of balanced gain and loss into the system via a complex coupling to the environment. This will be an analytical and numerical analysis of the dynamical behaviour of the system, and a study of the resulting sensitivity to rotation measurements. Numerical analysis of the multimode problem may also be done using the Truncated Wigner method.

Knowledge of many body quantum mechanics may be useful.

Experience with numerical modelling may be useful.