The parity operator: Applications in quantum metrology

In this paper, the authors review the use of parity as a detection observable in quantum metrology and introduce some original findings with regard to measurement resolution in Ramsey spectroscopy and quantum nondemolition measures of atomic parity. Parity was first introduced in the context of Ramsey spectroscopy as an alternative to atomic state detection. It was later adapted for use in quantum optical interferometry where it has been shown to be the optimal detection observable saturating the quantum Cram & eacute;r-Rao bound for path symmetric states. The authors include a brief review on the basics of phase estimation and the connection between parity-based detection and the quantum Fisher information as it applies to quantum optical interferometry. The authors also discuss the efforts made in experimental methods of measuring photon-number parity and close the paper with a discussion on the use of parity, leading to enhanced measurement resolution in multi-atom spectroscopy. The authors show how this may be of use in the construction of high-precision multi-atom atomic clocks.