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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Polarization coherent states in quantum optics: quasi-probability functions and geometric phases

V. P. Karassiov, Vladimir Leonardovich Derbov, Sergue Il'ich Vinitsky

Published May 3, 1994• 2 citations
Publisher

Abstract

Polarization coherent states (PCS) are considered as generalized coherent states of SU(2)p group of the polarization invariance of the light fields. In terms of PCS the polarization quasi probability functions are defined, which determine the quasi classical description of the statistical polarization properties of quantum light fields. The geometric phases of PCS are introduced in a way analogous to that used in the classical polarization optics.

DOI
10.1117/12.175142

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Polarization coherent states (PCS) are considered as generalized coherent states of SU(2)p group of the polarization invariance of the light fields. In terms of PCS the polarization quasi probability functions are defined, which determine the quasi classical description of the statistical polarization properties of quantum light fields. The geometric phases of PCS are introduced in a way analogous to that used in the classical polarization optics.
Polarization coherent states (PCS) are considered as generalized coherent states of SU(2)pSU(2)_pSU(2)p​ group of the polarization invariance of the light fields. The geometric phases of PCS are introduced in a way, analogous to that used in the classical polarization optics.
Within the new description of the polarization structure of quantum light (given in Part I) some types of generalized coherent states related to the polarization SU(2) group are examined. With their help we give a quasiclassical description of polarization properties of light fields and discuss the concept of squeezing and uncertainty relations for multimode light in the polarization quantum optics. As a consequence, a new classification of polarization states of quantum light is obtained. We also derive geometric phases acquired by different quantum light beams transmitted through "polarization rotators".
Quantum optics entails polarization properties that cannot be fully described by the classical Stokes parameters. In this work, we characterize the polarization of classical as well as quantum fields by means of a probability distribution on the Poincar\'e sphere. This serves to define the degree of polarization of a field state as the distance between the corresponding polarization distribution and the uniform distribution representing unpolarized light. We apply this definition to relevant quantum field states such as SU(2) coherent, squeezed, number, and phase states.
The geometric phase is studied for quantum polarized light described by an SU(2) coherent state. This is revealed by using quantum interference. The SU(2) coherent state is constructed from the quantized Stokes parameters. The quantum interferometry is arranged by the evolution operator implemented by the Hamiltonian inspired from the birefringence of the Faraday and Kerr effect. The geometric phase is given by the coherent state path integral. In particular, by considering a resonant Hamiltonian, the geometric phase is extracted from the total factor that consists of both geometric and dynamical phases. This extraction forms the basis of an experimental way to detect the geometric phase.
The elementary quantum theory of quasi-classical states for mechanical harmonic oscillators is applied to the radiation oscillators describing light, and thus used to define quasi-classical states of light. These states are called “coherent”, because the expectation value of any normally ordered product of creation and annihilation operators factorizes for them. A theoretical discussion of possible sources for coherent states is followed by experimental evidence for their existence. The mathematical properties of coherent states, e.g., nonorthogonality and overcompleteness, are explained in order to use them to represent states and operators. These representations provide a suitable replacement for the classical phase space description of light, which is forbidden by the uncertainty principle. The quantum phase space approach leads to the definition of the Wigner distribution, the Q-function, the P-function, and Gaussian mixed states.