We propose a scheme that a dynamically evolving atom-molecule condensate maps onto an SU(1, 1) interferometer, which includes a nonlinear medium (nonlinear phase encoding). We give an analytical result of the phase uncertainty from the error propagation by measuring the particle number at the output and demonstrate the optimal quantum metrology, which is obtained with a time-reversal protocol. We show the phase sensitivity of the nonlinear medium with time-reversal protocol scales as 1/(2.1N2), which overcome the conventional sensitivity limit of 1/N. Finally, the effect of the poor particle resolution detection on the phase sensitivity is discussed.
We propose a simple scheme to realize the persistent spin-nematic squeezing in a spinor Bose-Einstein condensate by rapidly turning-off the external magnetic field at a time that maximal spin-nematic squeezing occurs. We observe that the optimal spinnematic squeezing can be maintained in a nearly fixed direction. For a proper initial magnetic field, the optimal squeezing can be obviously enhanced. We further construct a spin-mixing interferometer, where the quantum correlation of the squeezed state (generated by our scheme) is fully utilized in the phase measurement, and show the phase sensitivity of the interferometer has a significant enhancement.
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