Phase States in Quantum Optics

Constantin Brif, Y. Ben-Aryeh

A phase space for the single-mode light field is constructed by using optical phase variables. This phase-space formalism is directly connected to optical-phase-related operators. The phase-state basis \ensuremath{\Vert}\ensuremath{\theta}〉 is used to represent various quantum operators and states. Properties of the density operator \ensuremath{\rho}^ phase-state matrix elements P(\ensuremath{\theta},\ensuremath{\theta}')=〈\ensuremath{\theta}\ensuremath{\Vert}\ensuremath{\rho}^\ensuremath{\Vert}\ensuremath{\theta}'〉 and their relations to phase-related quasiprobability distributions are discussed. By using the phase representation, different types of number-phase intelligent states are analyzed.

S. Olivares

Pradeep K Kumar, Anil Prabhakar

We present a quantum mechanical model to evaluate the time evolution of quantum states of light in an electro-optic phase modulator (EOPM). The phase modulator is analogous to a multilevel atomic system with equally spaced energy levels, each of which corresponds to the sidebands of the phase modulated optical field. Using perturbation theory, we solve the equations governing the interaction of the optical field with a modulating field both with and without phase velocity mismatch. A unitary operator that evolves any given quantum state allows us to evaluate the response of EOPM for single photon, coherent and squeezed states. We apply these results to the analysis of frequency coded quantum key distribution scheme.

Takafumi Ono

Quantum metrology enables us to estimate optical phase shifts beyond the shot noise limit. Applications include quantum-enhanced biological measurement [1], microscopy [2] and gravitational wave detection[3]. For two-mode N-photon system, the NOON state can achieve the highest possible phase sensitivity where multi-photon coherence between two states significantly contributes to improving the phase sensitivity. Another alternative approach to improve the phase sensitivity by use of squeezed states. Squeezing is usually characterized by reducing the quantum noise of desired observable at the expense of increasing the quantum noise for its non-commute partner. Because shot-noise limits the phase sensitivity of any classical states, the reduced quantum noise can be used for improving the phase sensitivity. Here we experimentally study the phase sensitivity of an optical spin-squeezed state by using linear optics. We generated the optical spin-squeezed state using one photon subtraction from a down converted photon source. To implement the sub-shot noise measurement, we used multiplexed photon number resolving detectors so that we can reconstruct the photon number statistics of the state. In the talk, we will analyse the generated state in terms of both squeezing and phase sensitivity by using Fisher information.

I. A. Deryugin, A. A. Vishenskii, Vitaliy N. Kurashov