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International Conference on Quantum Information

Polarization correlations in quantum optics

Luis Lorenzo Sánchez-Soto, A. B. Klimov, Gunnar G. Bjork, Jonas Söderholm, Ulrik L. Andersen, Christoph Marquardt, Gerd Leuchs

Published Jan 1, 2011• 0 citations
Publisher

Abstract

The standard degree of polarization involves exclusively first-order moments of the Stokes variables. This may be sufficient for most classical problems, but for quantum fields higher-order correlations are crucial. We claim that a complete polarization characterization must involve a whole hierarchy of polarization degrees constructed order by order, as it happens in coherence theory. We present here a second-order degree and determine it experimentally.

DOI
10.1364/icqi.2011.qtuh2

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The standard degree of polarization involves exclusively first-order moments of the Stokes variables. This may be sufficient for most classical problems, but for quantum fields higher-order correlations are crucial. We claim that a complete polarization characterization must involve a whole hierarchy of polarization degrees constructed order by order, as it happens in coherence theory. We present here a second-order degree and determine it experimentally.
We propose an operational degree of polarization in terms of the variance of the Stokes vector minimized over all the directions of the Poincaré sphere. We examine the properties of this second-order definition and carry out its experimental determination. Quantum states with the same standard (first-order) degree of polarization are correctly discriminated by this new measure. We argue that a comprehensive quantum characterization of polarization properties requires a whole hierarchy of higher-order degrees.
We present a moment expansion for the systematic characterization of the polarization properties of quantum states of light. Specifically, we link the method to the measurements of the Stokes operator in different directions on the Poincar\'e sphere and provide a scheme for polarization tomography without resorting to full-state tomography. We apply these ideas to the experimental first- and second-order polarization characterization of some two-photon quantum states. In addition, we show that there are classes of states whose polarization characteristics are dominated not by their first-order moments (i.e., the Stokes vector) but by higher-order polarization moments.
We comprehensively review the quantum theory of the polarization properties of light. In classical optics, these traits are characterized by the Stokes parameters, which can be geometrically interpreted using the Poincaré sphere. Remarkably, these Stokes parameters can also be applied to the quantum world, but then important differences emerge: now, because fluctuations in the number of photons are unavoidable, one is forced to work in the three-dimensional Poincaré space that can be regarded as a set of nested spheres. Additionally, higher-order moments of the Stokes variables might play a substantial role for quantum states, which is not the case for most classical Gaussian states. This brings about important differences between these two worlds that we review in detail. In particular, the classical degree of polarization produces unsatisfactory results in the quantum domain. We compare alternative quantum degrees and put forth that they order various states differently. Finally, intrinsically nonclassical states are explored, and their potential applications in quantum technologies are discussed.
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.