Abstract
Spinor Bose-Einstein condensate is an ideal candidate for implementing the many-body entanglement, quantum measurement and quantum information processing owing to its inherent spin-mixing dynamics. Here we present a system of an 87Rb atomic spin-1 Bose-Einstein condensate coupled to an optical ring cavity, in which cavity-mediated nonlinear interactions give rise to saddle points in the semiclassical phase space, providing a general mechanism for exponential fast scrambling and metrological gain augment. We theoretically study metrological gain and fidelity out-of-time-ordered correlator based on time-reversal protocols and demonstrate that exponential rapid scrambling dynamics can enhance quantum metrology. In addition, we use the out-of-time-ordered correlator to probe dynamical phase transitions. This work is useful to understand the intrinsic relation between the concepts from different subfields of quantum science.
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