Quantum Phase Estimation Based On Nonlinear Interferometer And Nonlinear Phase Shifter

Parametric amplifiers and nonlinear phase shifters can be used to improve the phase sensitivity and quantum Fisher information of interferometer so that they are widely concerned.Based on the advantages of these two nonlinear optical devices,in this thesis we have proposed two schemes for further improving the phase sensitivity and quantum Fisher information.Specially,based on the homodyne detection,we studied the phase sensitivity and the effect of photon losses on the phase sensitivity.With the help of the characteristic function method and the technique of integration within operator product,the quantum Fisher information of the interferometer and the effect of the photon losses on the quantum Fisher information are investigated.The specific research works of this paper can be summarized as follows:Firstly,we proposed an improved nonlinear interferometer(MNI)by combining the balanced optical beam divider(BBS),parametric amplifier(OPA)and nonlinear phase shifter.Then,we use coherent and even coherent states as input states,and perform homodyne detection at one output port of MNI to obtain phase sensitivity.The results show that the introduction of nonlinear phase shifter can not only improve the phase sensitivity,but also effectively suppress the decoherence caused by photon loss.Compared with the BBS + OPA scheme with a linear phase shifter and the traditional Mach Zehnder interferometer(MZI)with a nonlinear phase shifter,the phase sensitivity of MNI scheme is the best.Interestingly,although the SNR of BBS+ OPA scheme is not improved,the introduction of nonlinear phase shifter to the above scheme can further stimulate the performance of OPA and improve the phase accuracy of interferometer.Secondly,we proposed a theoretical scheme for improving the phase sensitivity and the quantum Fisher information by introducing Kerr nonlinear phase shift into the traditional SU(1,1)interferometer.Based on the homodyne detection,the phase sensitivity and quantum Fisher information are studied by selecting the coherent state and the vacuum state as the input states.The influence of photon loss on the phase sensitivity and quantum Fisher information is also considered.The results show that compared with the traditional SU(1,1)interferometer,the introduction of Kerr nonlinear phase shift can not only improve the super-resolution,but also improve the phase sensitivity and quantum Fisher information,even close to the super Heisenberg limit in an ideal case.In addition,the influence of photon losses inside the interferometer on the phase sensitivity is greater than that outside the interferometer under the same parameters.The introduction of Kerr nonlinear phase shift can improve the robustness of the interferometer.Interestingly,due to the introduction of nonlinear phase elements,this scheme shows the obvious advantage of low-cost input resources in obtaining higher phase sensitivity and larger quantum Fisher information.