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Journal of Experimental and Theoretical Physics

Polarization transformations of multimode light fields

V. P. Karassiov, S. P. Kulik

Published Feb 1, 2007• 12 citations
Publisher

Abstract

The concept of P -quasispin is used as a framework for developing a formalism for polarization transformation by means of lossless polarization-changing optical elements for both classical and quantum multimode light fields. As an example, a classification of transformations of this kind is presented for two-mode biphoton fields that implement the information-theoretic concepts of qutrit and ququart (quantum systems in three-and four-dimensional Hilbert states, respectively).

DOI
10.1134/s1063776107010049

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The concept of P -quasispin is used as a framework for developing a formalism for polarization transformation by means of lossless polarization-changing optical elements for both classical and quantum multimode light fields. As an example, a classification of transformations of this kind is presented for two-mode biphoton fields that implement the information-theoretic concepts of qutrit and ququart (quantum systems in three-and four-dimensional Hilbert states, respectively).
Conceptual and operational aspects of the description of the polarization of light in classical and quantum optics are discussed. Primary emphasis is placed on the concept of P -quasispin, which ensures an adequate analysis for arbitrary quantum light fields. In terms of this concept, the polarization density matrix, which is obtained by reduction of the total field density operator and which completely describes the polarization state of quantum radiation, as well as the operational (measured in polarization experiments) characteristics and the transformations of the polarization dynamics, are determined. Applications of the formalism developed to biphoton optics are discussed.
The notion and main conceptual and operational characteristics of the polarization state of quantum radiation are defined within the framework of the P - quasispin formalism developed earlier by the author. This state is shown to be described fully by the polarization density matrix obtained via reducing the field density operator. Basic operational quantities (quantum polarization degree, polarization "noises" , etc.), measured in quantum experiments and displaying peculiarities of polarization states, are defined with the help of P - quasispin components. The idea and features of polarization nonclassical states of quantum light are discussed. In this approach a series of nonclassical states of the biphoton radiation, manifesting unusual (for classical optics) polarization features, are analyzed. Some of applied possibilities of such states are briefly discussed.
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.
Most protocols of quantum information transmission are based on qubits, or two-level quantum systems. However, in certain cases, it is reasonable to use quantum systems of higher dimensionality, such as, for instance, qutrits - three-level systems. In the present paper, it is shown that single-mode entangled pairs of polarized photons (biphotons) can be used for this purpose. Polarization state of a single-mode biphoton is considered and its representation on the Poincare sphere is suggested. An orthogonality criterion for two biphotons in arbitrary polarization states is formulated. Experiments on polarization transformations of biphotons are described. Finally, propagation of biphotons through fibres is considered.