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Quantum metrology with rotating matter waves in different geometries

A promising practical application of entanglement is metrology, where quantum states can be used to make measurements beyond the shot noise limit. Here we consider how metrology schemes could be realised using atomic Bose-Einstein condensates (BECs) trapped in different potentials. In particular, we show that if a trapped BEC is rotated at just the right frequency, it can undergo a quantum phase transition characterised by large-scale entanglement spreading across the system. This simple process of stirring can generate interesting quantum states such as macroscopic superpositions of all the atoms flowing in opposite directions around a ring-shaped potential. We consider different trapping potentials and show how this leads to different entangled states. In particular, we find that by reducing the dimensionality of the system to one or two dimensions, it is possible to generate entangled states that are remarkably robust to the loss of atoms and so are ideally suited to precision measurement schemes.