| In this thesis we investigate the precise optical phase measurement with an SU(1,1) nonlinear interferometer. Precision metrology has been a well-known problem and has many applications, the gravitational wave detection most notably. This thesis is strung together by a common underlying theme-how to improve the sensitivity of estimation of an unknown parameter by exploiting the various schemes in an SU(1,1) interferometer, such as, different input states and quantum Cramer-Rao bound. What we studied includes:We study the phase sensitivity of an SU(1,1) interferometer with coherent and squeezed vacuum input state with homodyne detection. Our results indicate that the phase sensitivity with homodyne detection can approach the Heisenberg limit if the relation among the intensity of coherent state, squeezing parameter of the squeezed vacuum input, and the optical parametric strength satisfies some certain condition. The corresponding requirment is also present. Compared with intensity detection, homodyne detection has a slightly better phase sensitivity under some certain condition. Last, we investigate the effect of loss on the phase sensitivity of an SU(1,1) interferometer.We investigate the performance of an SU(1,1) interferometer with coherent and squeezed vacuum input state with parity detection. We find that parity detecion has a super-resolution signal. Compared with homodyne detection and intensity detection, parity detection has a slightly better phase sensitivity under some certain condition. Later, we also investigate the effect of loss on the phase sensitivity in an SU(1,1) interferometer.We compare among intensity detection, homodyne detection, and parity detection. However, it is not convenient to study all kinds of detection methods. Here, we study the quantum Cramer-Rao bound in an SU(1,1) interferometer which gives an ultimate estimation precision limit. Later, we present the quantum Cramer-Rao bound in an SU(1,1) interferometer with various input states. |
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