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arXiv:quant-ph/9503011

Polarization Structure of Quantum Light Fields: A New Insight. 2: Generalized Coherent States, Squeezing and Geometric Phases

V. P. Karassiov

Published Mar 13, 1995• 0 citations
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Abstract

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".

DOI
10.48550/arxiv.quant-ph/9503011

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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".
The concept of squeezing and uncertainty relations are discussed for multimode quantum light with the consideration of polarization. Using the polarization gauge SU(2) invariance of free electromagnetic fields, we separate the polarization and biphoton degrees of freedom from other ones, and consider uncertainty relations characterizing polarization and biphoton observables. As a consequence, we obtain a new classification of states of unpolarized (and partially polarized) light within quantum optics. We also discuss briefly some interrelations of our analysis with experiments connected with solving some fundamental problems of physics.
A new consequent description of the polarization structure of light within the framework of quantum optics is given by using the polarization gauge SU(2) invariance of free electromagnetic fields and a related concept of the polarization (P) spin. Within this approach the quantum light may be thought as a mixture of the usual polarized photons and unpolarized biphotons. New classes of unpolarized light states generated by P-scalar biphotons are examined. Possible applications are briefly discussed.
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.
In our paper we consider the non-classical behaviour of both the Hermitian (observable) Stokes parameters of light and the phase difference of two modes that describe the quantum polarization states of optical field. To characterize the degree of polarization of light we introduce a new quantity taking into account the quantum properties of different quantum states of two orthogonally polarized modes. The problem of determination of the phase difference in two modes of optical field for the quantum polarization states of light is discussed. To describe in general such a quantum field we introduce two pairs of the phase operators: the phase angles for the Stokes parameters of light in a three-dimensional picture of the Poincaré sphere. We also consider a special type of the eight-port polarization interferometer (polarimeter) for simultaneous homodyne detection of both the Stokes parameters of light and the polarization phase operators and their fluctuations as well. Using an anisotropic (spatioperiodic) Kerr-like nonlinear medium associated with the polarization interferometer we could generate and also observe the polarization-squeezed phase states of light. The fluctuations in the phase difference between two orthogonally polarized modes for these non-classical states are less than the fluctuations for light in coherent state.