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Quantum Electronics and Laser Science Conference

Continuous variable Bell-type correlations from two bright squeezed beams

Elanor H. Huntington, Timothy C. Ralph

Published Jan 1, 2002• 0 citations
Publisher

Abstract

Summary form only given. Drawing on recent advances in the treatment of continuous variable systems, we propose two systems that can be used to observe Bell-type correlations between the continuous variables of their sub-systems. A set of polarisation dependent measurements of the quadrature amplitude and phase of a system can be used to construct a correlation parameter that we shall denote B. We take B > 2 to indicate Bell-type (or strong, nonclassical) correlations, which may be used as a resource in quantum information experiments.

DOI
10.1109/qels.2002.1031311

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Summary form only given. Drawing on recent advances in the treatment of continuous variable systems, we propose two systems that can be used to observe Bell-type correlations between the continuous variables of their sub-systems. A set of polarisation dependent measurements of the quadrature amplitude and phase of a system can be used to construct a correlation parameter that we shall denote B. We take B > 2 to indicate Bell-type (or strong, nonclassical) correlations, which may be used as a resource in quantum information experiments.
In this paper we propose two surprisingly simple optical systems that display Bell-type correlations between the continuous variables of their subsystems. We first discuss how these two systems may be used to construct Bell-type correlations from two bright, amplitude-squeezed sources. Then the experimental viability of these systems is analyzed. Issues such as the conditions under which the systems display Bell correlations, sources of nontechnical as well as technical noise, signal-to-noise ratio and losses are discussed. Based on this discussion, we conclude that both of these systems are currently experimentally viable.
In this paper we present a scheme in which the amplitude-quadrature difference and phase-quadrature difference of two bright nonclassical beams serve as a pair of observed complementary variables that can be measured directly and can form a new squeezed state. Mixing such two quadrature-difference squeezed-state beams on a beam splitter produces characteristic of the Einstein-Podolsky-Rosen quantum entanglement. The experimental schemes producing such nonclassical beams and its possible applications in quantum information are discussed.
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 have experimentally demonstrated the efficient creation of highly entangled bipartite continuous variable polarisation states. Exploiting an optimised scheme for the production of squeezing using the Kerr non-linearity of a glass fibre we generated polarisation squeezed pulses with a mean classical excitation in S3. Polarisation entanglement was generated by interfering two independent polarisation squeezed fields on a symmetric beam splitter. The resultant beams exhibit strong quantum noise correlations in the dark S1 - S2 polarisation plane. To verify entanglement generation, we characterised the quantum correlations of the system for two different sets of conjugate Stokes parameters. The quantum correlations along the squeezed and the anti-squeezed Stokes parameters were observed to be -4.1 +/- 0.3 dB and -2.6 +/- 0.3 dB below the shot noise level respectively. The degree of correlations was found to depend critically on the beam splitting ratio of the entangling beam splitter. Carrying out measurements on a different set of conjugate Stokes parameters, correlations of -3.6 +/- 0.3 dB and -3.4 +/- 0.3 dB have been observed. This result is more robust against asymmetries in the entangling beam splitter, even in the presence of excess noise.
For measurements describable by a discrete set of possibilities, numerous demonstrations of the violation of Bell's inequalities have been reported in optical physics based on observations of polarization correlations for photon pairs. By contrast for observables with a continuous spectrum, there appears to be no general inequalities corresponding to those of Bell and no experimental realization of the original Einstein-Podolsky-Rosen paradox. Following Reid and Drummond,1 we are attempting to demonstrate the EPR paradox in the context of the measurement of continuous quantum variables with a subthreshold optical parametric oscillator operated in a frequency degenerate but polarization nondegenerate mode. In this case, the EPR paradox is formulated in terms of two sets of quadrature phase amplitudes for the spatially separated signal and idler fields. As the parametric gain is increased toward threshold, the quadrature amplitudes of the signal and idler beams become increasingly faithful quantum copies of one another. Our measurements of quadrature amplitudes are carried out using independent balanced homodyne detectors at two sites. When operated for the detection of squeezing at one site, noise reductions of 4 dB relative to the vacuum state limit are observed, which is most encouraging since noise reductions >3 dB in the difference photocurrent from the two sites are sufficient for inference at a distance of a signal observable from a measurement of the corresponding idler variable.