Decoherence Of Photon-added Schrodinger Cat States In Thermal Environment And Application Of Quantum Metrology

On the one hand, we analyze the statistical properties and decoherence of thefield states produced by adding any number of photons to the Schrodinger Cat states(SCSs) in a thermal environment. It is found that the normalization factor of PA-SCSis the Hermite polynomial of the coherent factor α. The statistical properties anddecoherence is discussed by deriving analytically the time evolution of theQ-function, Wigner function and the photon-number distribution. It is shown that thesingle photon-added even SCSs, the Wigner function is always positive in the wholephase space when κt exceeds the threshold value1/2In[(2n|+2)/(2n|+1)]. Thisimplies that the single photon-added even SCSs possesses a robustness due to thepresence of photon-addition, which can also be seen from the point of view of thevolume of negative region of Wigner function.On the other hand, we study the quantum interference and the phase estimationwith parity detection through Mach-Zender interferometer with an arbitrary-photonFock state and an even coherent state as two inputs. The parity signal is moresuper-resolved with the increase of m,nc values. In addition, the phase sensitivity hassuperior sensitivity in the vicinity of φ=0, and reaches below shot-noise limitbetween some certain area, also approach the Heisenberg limit.