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arXiv:1603.09019 · Physical Review A

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

Dong Li, Bryan Gard, Yang Gao, Chun-Hua Yuan, Weiping Zhang, Hwang Lee, Jonathan P. Dowling

Published Dec 19, 2016• 105 citations
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Abstract

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

DOI
10.1103/physreva.94.063840

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Mach-Zehnder interferometry based on mixing the coherent and the squeezed vacuum states of light has Heisenberg limited capabilities for phase estimation. This is also, because the quantum Cramer-Rao bound on sensitivity of phase estimation with the above interferometric scheme reaches the Heisenberg limit when the inputs are mixed in hear equal proportions. We show that a detection strategy based on the measurement of parity of photon number in one of the output modes of the interferometer saturates the quantum Cramer-Rao bound of the interferometric scheme, and therefore- as a consequence- hits the Heisenberg limit when the inputs are mixed in equal intensities.