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arXiv:quant-ph/0208103 · Physical Review A

Stokes-operator-squeezed continuous-variable polarization states

Roman Schnabel, Warwick P. Bowen, Nicolas Treps, Timothy C. Ralph, Hans‐A. Bachor, Ping Koy Lam

Published Jan 28, 2003• 50 citations
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Abstract

We investigate nonclassical Stokes-operator variances in continuous-wave polarization-squeezed laser light generated from one and two optical parametric amplifiers. A general expression of how Stokes-operator variances decompose into two-mode quadrature operator variances is given. Stokes parameter variance spectra for four different polarization-squeezed states have been measured and compared with a coherent state. Our measurement results are visualized by three-dimensional Stokes-operator noise volumes mapped on the quantum Poincar\'e sphere. We quantitatively compare the channel capacity of the different continuous-variable polarization states for communication protocols. It is shown that squeezed polarization states provide 33% higher channel capacities than the optimum coherent beam protocol.

DOI
10.1103/physreva.67.012316

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We investigate nonclassical Stokes-operator variances in continuous-wave polarization-squeezed laser light generated from one and two optical parametric amplifiers. A general expression of how Stokes-operator variances decompose into two-mode quadrature operator variances is given. Stokes parameter variance spectra for four different polarization-squeezed states have been measured and compared with a coherent state. Our measurement results are visualized by three-dimensional Stokes-operator noise volumes mapped on the quantum Poincar'e sphere. We quantitatively compare the channel capacity of the different continuous-variable polarization states for communication protocols. It is shown that squeezed polarization states provide 33% higher channel capacities than the optimum coherent beam protocol.
A concept of polarization entanglement for continuous variables is introduced. For this purpose the Stokes-parameter operators and the associated Poincar\'e sphere, which describe the quantum-optical polarization properties of light, are defined and their basic properties are reviewed. The general features of the Stokes operators are illustrated by evaluation of their means and variances for a range of simple polarization states. Some of the examples show polarization squeezing, in which the variances of one or more Stokes parameters are smaller than the coherent-state value. The main object of the paper is the application of these concepts to bright squeezed light. It is shown that a light beam formed by interference of two orthogonally polarized quadrature-squeezed beams exhibits squeezing in some of the Stokes parameters. Passage of such a primary polarization-squeezed beam through suitable optical components generates a pair of polarization-entangled light beams with the nature of a two-mode squeezed state. Implementation of these schemes using the double-fiber Sagnac interferometer provides an efficient method for the generation of bright nonclassical polarization states. The important advantage of these nonclassical polarization states for quantum communication is the possibility of experimentally determining all of the relevant conjugate variables of both squeezed and entangled fields using only linear optical elements followed by direct detection.
We report the first direct experimental characterization of continuous variable quantum Stokes parameters. We generate a continuous wave light beam with more than 3 dB of simultaneous squeezing in three of the four Stokes parameters. The polarization squeezed beam is produced by mixing two quadrature squeezed beams on a polarizing beam splitter. Depending on the squeezed quadrature of these two beams the quantum uncertainty volume on the Poincaré sphere becomes a "cigarlike" or "pancakelike" ellipsoid.
Results of experiments recently performed are reported, in which two optical parametric amplifiers were set up to generate two independently quadrature squeezed continuous wave laser beams. The transformation of quadrature squeezed states into polarization squeezed states and into states with spatial quantum correlations is demonstrated. By utilizing two squeezed laser beams, a polarization squeezed state exhibiting three simultaneously squeezed Stokes operator variances was generated. Continuous variable polarization entanglement was generated and the Einstein-Podolsky-Rosen paradox was observed. A pair of Stokes operators satisfied both the inseparability criterion and the conditional variance criterion. Values of 0.49 and 0.77, respectively, were observed, with entanglement requiring values below unity. The inseparability measure of the observed quadrature entanglement was 0.44. This value is sufficient for a demonstration of quantum teleportation, which is the next experimental goal of the authors.
We present methods of transforming the standard quadrature amplitude squeezing of a continuous-wave light beam to its Stokes parameters and transverse spatial modes statistics. These two states of light are called polarization squeezing and spatial squeezing, respectively. We present experimental results of the quadrature amplitude, polarization and spatial squeezing obtained with a common experimental setup based on optical parametric amplifiers. The transformations from quadrature amplitude to polarization and spatial squeezing are achieved with only simple linear optics.
Abstract We demonstrate experimentally a measurement scheme for the Stokes operators for the continuous-variable squeezed states of orbital angular momentum (OAM). An OAM squeezed state is generated by coupling a dim Hermite-Gauss HG01-mode quadrature-squeezed light beam with a bright HG10-mode coherent light beam on a 98/2 beam splitter. Using an asymmetric Mach–Zehnder interferometer with an extra Dove prism in one arm, we measured the three orbital Stokes operators of the OAM squeezed states with a self-homodyne detection and finally characterized their positions and noise on the orbital Poincaré sphere.
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.