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arXiv:0901.4813 · Physical Review A

Spatial-state Stokes-operator squeezing and entanglement for optical beams

Magnus T. L. Hsu, Warwick P. Bowen, Ping Koy Lam

Published Apr 23, 2009• 26 citations
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Abstract

The transverse spatial attributes of an optical beam can be decomposed into the position, momentum, and orbital angular momentum observables. The position and momentum of a beam are directly related to the quadrature amplitudes, while the orbital angular momentum is related to the polarization (spin) variables. In this paper, we study the quantum properties of these spatial variables, using a representation in the Stokes-operator basis. We propose a spatial detection scheme to measure all three spatial variables and, consequently, propose a scheme for the generation of spatial Stokes-operator squeezing and entanglement.

DOI
10.1103/physreva.79.043825

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The transverse spatial attributes of an optical beam can be decomposed into the position, momentum, and orbital angular momentum observables. The position and momentum of a beam are directly related to the quadrature amplitudes, while the orbital angular momentum is related to the polarization (spin) variables. In this paper, we study the quantum properties of these spatial variables, using a representation in the Stokes-operator basis. We propose a spatial detection scheme to measure all three spatial variables and, consequently, propose a scheme for the generation of spatial Stokes-operator squeezing and entanglement.
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.
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.
The entanglement of optical angular position and orbital angular momentum has become one of the important degrees of freedom for quantum information science. Quantum control of the two conjugate variables may provide a gate to control the production of the entanglement. Here, we theoretically and experimentally show that by controlling the transverse spatial coherence of the pump beam, one can modulate the strength of the quantum correlations between the angular position and orbital angular momentum in down-converted photon pairs. By determining the relation of the Einstein, Podolsky, and Rosen correlations with the transverse spatial coherence of the pump, the boundary of the entanglement can be determined. Our work shows that the transverse spatial coherence of the pump can act as a switch to control the production of quantum entanglement both for discrete and continuous conjugate variables and may provide another platform for the quantum control research field.
A light beam is said to be position squeezed if its position can be determined to an accuracy beyond the standard quantum limit. We identify the position and momentum observables for bright optical beams and show that position and momentum entanglement can be generated by interfering two position, or momentum, squeezed beams on a beam splitter. The position and momentum measurements of these beams can be performed using a homodyne detector with local oscillator of an appropriate transverse beam profile. We compare this form of spatial entanglement with split detection-based spatial entanglement.
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.
We report the first experimental characterization of the first-order continuous variable orbital angular momentum states. Using a spatially nondegenerate optical parametric oscillator (OPO) we produce quadrature entanglement between the two first-order Laguerre-Gauss modes. The family of orbital angular momentum modes is mapped on an orbital Poincaré sphere, where the mode's position on the sphere is spanned by the three orbital parameters. Using a nondegenerate OPO we produce squeezing of these parameters, and as an illustration, we reconstruct the "cigar-shaped" uncertainty volume on the orbital Poincaré sphere.