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Journal of Experimental and Theoretical Physics Letters

P-quasispin formalism in polarization optics

V. P. Karassiov

Published Feb 1, 2007• 8 citations
Publisher

Abstract

The polarization ( P ) quasispin formalism that ensures the effective analysis of the polarization of arbitrary quantum light fields is justified. New conceptual and operational characteristics of the polarization states of quantum radiation, as well as the transformations of their polarization dynamics, are determined within the framework of this approach.

DOI
10.1134/s0021364006240027

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The polarization ( P ) quasispin formalism that ensures the effective analysis of the polarization of arbitrary quantum light fields is justified. New conceptual and operational characteristics of the polarization states of quantum radiation, as well as the transformations of their polarization dynamics, are determined within the framework of this approach.
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.
We present a quantum analysis of two-mode single-photon states based on the probability distributions of the optical field strength (or position quadrature) in order to describe their quantum polarization characteristics, where polarization is understood as a significative confinement of the optical field-strength values on determined regions of the two-mode optical field-strength plane. We will show that the mentioned probability distributions along with the values of quantum Stokes parameters allow us to characterize the polarization of a two-mode single-photon state, in an analogous way to the classical case, and to distinguish conceptually between mixture and partially polarized quantum states; in this way, we propose a simple definition of the quantum polarization degree based on the recent concept of distance measure to an unpolarized distribution, which gives rise to a depolarization degree equivalent to an overlapping between the probability distribution of the quantum state and a non-polarized two-mode Gaussian distribution. The work is particularly intended to university physics teachers and graduate students as well as to physicists and specialists concerned with the issue of optical polarization.
The usefulness of Brown's polarization formalism as a paradigm for the dynamics of analogous linear systems is demonstrated. By connecting the rotations of the Lorentz group with birefringence and the Lorentz group boosts with dichroism, this formalism has offered closed-form solutions, expressed in the language of the Lorentz group, for the 4 X 4 Mueller matrices of polarization optics. First, we discuss the dynamics of a generic two-state system satisfying a Schrodinger-like differential equation. This equation is cast into a four dimensional form. Next, we show the solution of the latter to be a Lorentz transformation. Then, we analyze several specific examples. The examples include: (1) precession, (2) a magnetic dipole in a magnetic field, (3) a charged particle in an electric field, and (4) time- independent perturbation theory with phenomenological damping. We argue the approach of Brown's formalism provides a convenient conceptual framework to describe the physics and to interpret the measurement results of such systems. In addition, this approach broadens the role of the Lorentz group to areas other than special relativity and electromagnetic scattering.
We report on two quantum polarization experiments. The first one shows that three geometrical rotations can in principle be distinguished with certainty using two photons. The second experiment shows quantum polarization properties of classically unpolarized light. We outline a new treatment of polarization in quantum optics. Our formalism differs from the usual quantum description, which uses the Stokes operators. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.