Improving the phase sensitivity of an SU (1, 1) interferometer via a nonlinear phase encoding

Abstract

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.