Negativity of Wigner function and phase sensitivity of an SU(1,1) interferometer

Both the negativity of Wigner function and the phase sensitivity of an SU(1,1) interferometer are investigated in this paper. In the case that the even coherent state and squeezed vacuum state are input into the interferometer, the Heisenberg limit can be approached with parity detection. At the same time, the negativity volume of Wigner function of detection mode comes entirely from the input state and varies periodically with the encoding phase. In addition, the negativity volume of Wigner function is positively correlated with the phase sensitivity of the SU(1,1) interferometer. The positive correlation may mean that the non-classicality indicated by negative Wigner function is a kind of resource that can verify some related research results of phase estimation.