Parity measurements in optical interferometry and tests of quantum mechanics

We study the use of parity in context of high resolution interferometry. Maximally entangled states play a crucial role in the applications of the Heisenberg-limited interferometry; it enhances the sensitivity of the detection of the gravitational waves. Interferometry with maximally entangled states cannot be performed by simply subtracting the output photocounts as in standard quantum interferometry. Instead, one must perform parity measurements on only one of the output beams. We use the same technique to show that with twin Fock input states in a Mach-Zehnder interferometer, the phase sensitivity approaches the Heisenberg limit for large photon number. Then we study the generations of maximally entangled states and states of superposition of maximally entangled states using nonlinear interferometry. Nonlinear interferometers are Mach-Zehnder interferometers with Kerr media in either one or both arms. We refer to these devices, respectively, as the asymmetric and symmetric nonlinear interferometers. In the asymmetric case, with one input mode in the vacuum, it is possible to generate maximally entangled states or superpositions of such states. We consider the device as a resource of entangled states for applications to Heisenberg-limited interferometry. We also consider the nonlinear four-wave mixer as a resource for superpositions of only even input states. Considering both even coherent states and squeezed vacuum states as inputs; we study their applications to high resolution interferometry.; We then study parity measurements. We show that the symmetric nonlinear interferometer, with the vacuum state in one input mode, may be used to perform parity measurements. The same device is shown to produce, with an input coherent state and upon projective measurements, even or odd coherent states, examples of the Schrodinger cat states. We also study quantum non-demolition parity measurements using cross-Kerr medium. We show that one can determine parity of a state without destroying it, using cross-Kerr medium along with homodying measurements. With the same technique we can construct some Schrodinger cat states.; We also study parity measurements to test quantum mechanics against the local realistic theories. To that end, we propose an optical realization of the Greenberger, Horne, Zeilinger (GHZ) state. The optical GHZ states in this case are three-mode entangled coherent states and the relevant observable used to perform test of quantum mechanics against local realistic theories is photon number parity. The amplitudes of the coherent states need by maccoscopic if significant losses are involved by may be macroscopic if losses are minimal. We propose a method of generating the required GHZ state that amounts to an extension of a proposal previously discussed by C. C. Gerry (Phys. Rev A 59, 4095 (1999)) for generating macroscopic superposition states of traveling wave fields.