Adil Benmoussa

Parity measurements, Heisenberg-limited phase estimation, and beyond

We review the use of parity measurements to obtain Heisenberg-limited phase shift measurements from interferometry performed with maximally path entangled two mode states containing N photons, contrasting this measure with the method of coincidence detection which requires a number of such detections that scales with N. For large N, coincidence measurements will become impractical. In contrast, the parity method we propose is independent of N. In addition, with the parity approach, one can use an entanglement of a coherent state and the vacuum to approach the Heisensberg limit of phase resolution without the requirement of first producing a Fock state of large photon number. We also show in a very simple way, using Maximally entangled states and parity measurements that it is possible to go beyond the Heisenberg limit if the phase shifts are generated by a nonlinear Kerr-like interaction.

Entangled Coherent States, Heisenberg-Limited Metrology, and Related Issues

We discuss the generation of two mode maxinally entangled coherent states using a weak nonlinear medium. We then discuss their applications to quantum metrology (Heisenberg-limited interferometry), quantum lithography and violations of Bell-type inequalities.

Proposal for a macro/meso-scopic Greenberger-Horne-Zeilinger test of quantum mechanics with entangled optical travelling-wave coherent states

An optical realization of the Greenberger, Horne, Zeilinger (GHZ) state is proposed for testing local realistic theories. The optical GHZ states in this case are three-mode entangled coherent states and the relevant observable used to perform tests of quantum mechanics against local realistic theories is photon number parity. The amplitudes of the coherent states need to be mesoscopic if significant losses are involved but may be macroscopic if losses are minimal. A method is proposed for generating the required GHZ state that amounts to an extension of a proposal previously discussed (C.C. Gerry, Phys. Rev. A 59 4095 (1999)) for generating macroscopic superposition states of travelling wave fields.

Dark states of two-mode quantized fields in two-channel models: competing k- and l-photon processes

We examine the properties of two-mode field states |ξkl satisfying the eigenvalue problem , subject to the condition that they are also eigenstates of the operator . For the special case where k = l = 1, the resultant states are just the SU(2) coherent states of a two-mode field. The states |ξkl may arise as population trapping states, also known as dark states, in models involving competitive k- and l-photon processes.

Single-mode squeezed vacuum states as approximate Schrödinger phase cats: relation to SU(1,1) phase operators

We study the eigenstates of the square of the phase operator for a single-mode field, and show that they are given as superpositions of macroscopically distinguishable phase states, which we call Schrodinger phase cats, the phase states being eigenstates of the phase operator. Those solutions that are also eigenstates of the parity operator with even parity are shown to be very similar to the squeezed vacuum states over a range of relevant parameters. Thus, it is possible to consider some squeezed vacuum states as approximate Schrodinger phase-cat states. We discuss the connections to the phase states of the SU(1, 1) phase operators for various realizations and representations.