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We theoretically investigate the phase sensitivity with parity detection onan SU(1,1) interferometer with a coherent state combined with a squeezed vacuumstate. This interferometer is formed with two parametric amplifiers for beamsplitting and recombination instead of beam splitters. We show that thesensitivity of estimation phase approaches Heisenberg limit and give thecorresponding optimal condition. Moreover, we derive the quantum Cram\'er-Raobound of the SU(1,1) interferometer.

Phase sensitivity at the Heisenberg limit in an SU(1,1) interferometer via parity detection