The parity operator in quantum optical metrology

Abstract

Abstract Photon number states are assigned a parity of +1 if their photon number is even and a parity of −1 if odd. The parity operator, which is minus one to the power of the photon number operator, is a Hermitian operator and thus a quantum mechanical observable although it has no classical analogue, the concept being meaningless in the context of classical light waves. In this paper we review work on the application of the parity operator to the problem of quantum metrology for the detection of small phase shifts with quantum optical interferometry using highly entangled field states such as the so-called N00N states, and states obtained by injecting twin Fock states into a beam splitter. With such states and with the performance of parity measurements on one of the output beams of the interferometer, one can breach the standard quantum limit, or shot-noise limit, of sensitivity down to the Heisenberg limit, the greatest degree of phase sensitivity allowed by quantum mechanics for linear phase shifts. Heisenberg limit sensitivities are expected to eventually play an important role in attempts to detect gravitational waves in interferometric detection systems such as LIGO and VIRGO. Keywords: quantum metrologyparity operatorquantum optical interferometry Acknowledgements CCG gratefully wishes to thank A. Benmoussa and R.A. Campos for collaborations on this work over the past decade, and for conversations on quantum optical metrology, Mark Hillery, Hwang Lee, and Jon Dowling. The work has been funded by TheResearch Corporation, The National Science Foundation, The Army Research Office, and grants from PSC-CUNY.

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