Quantum Fisher Information On An Su(1,1) Interferometer

In recent years,quantum enhanced metrology can obtain the higher precision than purely classical approaches,which has received a lot of attention.In particular,the SU(1,1)nonlinear interferometer is applied to improve the sensitivity of phase estimation,which will become a new breakthrough in precision measurement.In this paper,we mainly study the quantum Fisher information(QFI)in SU(1,1)interferometer,and discuss how to improve the sensitivity of phase estimation.Firstly,we theoretically study the QFI of the SU(1,1)interferometer with phase shifts in two arms by coherent(g)squeezed vacuum state input,and give the comparison with the result of phase shift only in one arm.Different from the traditional Mach-Zehnder interferometer,the QFI of single arm case for an SU(1,1)interferometer can be slightly higher or lower than that of double arms case?which depends on the intensities of the two arms of the interferometer.For coherent(?)squeezed vacuum state input and with a fixed mean photon number,the optimal sensitivity is achieved with a squeezed vacuum input in one mode and the vacuum input in the other.And then,we further theoretically derive the lower and upper bounds of QFI of an SU(1,1)interferometer whatever the input state chosen,hence we get the lower bound of phase estimation.According to the QFI,phase estimation of the quantum enhancement is dominant mainly by the intramode correlations which is indicated by the Mandel Q-parameter,rather than the intermode correlations.We use the subtraction of photons from the squeezed vacuum state as an example.The average photon number of the field is increased by changing the super Poisson distribution of the probe field based on photon subtraction,then the QFI of phase is improved as well as the sensitivity of phase estimation.