Spin-orbit coupled interferometry with ring–trapped Bose–Einstein condensates: supporting data

We propose a method of atom-interferometry using a spinor Bose–Einstein (BEC) and the well-established experimental technique of time-varying magnetic fields as a coherent beam-splitter. Our protocol creates long-lived superpositional counterflow states, which are of fundamental interest and can be made sensitive to both the Sagnac effect and magnetic fields on the sub micro-Gauss scale. We split a ring-trapped condensate, initially in the m f = 0 hyperfine sub-level, into superpositions of both internal spin state and condensate superflow, which are spin-orbit coupled. After interrogation a relative phase accumulation can be inferred from a population transfer to the m f = ±1 states. Our protocol maximises the classical Fisher information, and owing to the adiabatic splitting it may be a good candidate for developing quantum enhanced interferometry schemes. We present numerical and analytical treatments of our system.