Active SU(1,1) atom interferometry

Active interferometers use amplifying elements for beamsplitting and recombination. Weexperimentally implement such a device by using spin exchange in a Bose-Einstein condensate. The two interferometry modes are initially empty spin states that get spontaneously populated in the process of parametric amplification. This nonlinear mechanism scatters atoms into bothmodes in a pairwise fashion and generates a non-classical state. Finally, amatched second period of spin exchange is performed that nonlinearly amplifies the output signal and maps the phase onto readily detectable firstmoments. Depending on the accumulated phase this nonlinear readout can reverse the initial dynamics and deamplify the entangled state back to empty spin states. This sequence is described in the framework of SU(1,1) modetransformations and compared to the SU(2) angularmomentum description of passive interferometers.