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arXiv:quant-ph/0302083 · Journal of Optics B Quantum and Semiclassical Optics

A pulsed source of continuous variable polarization entanglement

Oliver Gl ckl, Joel Heersink, Natalia Korolkova, Gerd Leuchs, Stefan Lorenz

Published Aug 1, 2003• 22 citations
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Abstract

We have experimentally demonstrated polarization entanglement using continuous variables in an ultra-short pulsed laser system at the telecommunications wavelength of 1.5µm. Exploiting the Kerr non-linearity of a glass fibre we generated polarization squeezed pulses with Ŝ 2 as the only non-zero Stokes parameter, thus Ŝ 1 and Ŝ 3 being the conjugate pair. Polarization entanglement was generated by interference of the polarization squeezed field with a vacuum on a 50:50 beamsplitter. The two resultant beams exhibit strong quantum noise correlations in Ŝ 1 and Ŝ 3 . The sum noise signal of Ŝ 3 was at the respective shot noise level and the difference noise signal of Ŝ 1 fell −2.9 dB below this value.

DOI
10.1088/1464-4266/5/4/355

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We have experimentally demonstrated polarization entanglement using continuous variables in an ultra-short pulsed laser system at the telecommunications wavelength of 1.5µm. Exploiting the Kerr non-linearity of a glass fibre we generated polarization squeezed pulses with Ŝ 2 as the only non-zero Stokes parameter, thus Ŝ 1 and Ŝ 3 being the conjugate pair. Polarization entanglement was generated by interference of the polarization squeezed field with a vacuum on a 50:50 beamsplitter. The two resultant beams exhibit strong quantum noise correlations in Ŝ 1 and Ŝ 3 . The sum noise signal of Ŝ 3 was at the respective shot noise level and the difference noise signal of Ŝ 1 fell −2.9 dB below this value.
We have experimentally demonstrated the efficient creation of highly entangled bipartite continuous variable polarization states. Exploiting an optimized scheme for the production of squeezing using the Kerr non-linearity of a glass fibre we generated polarization squeezed pulses with a mean classical excitation in . Polarization entanglement was generated by interfering two independent polarization squeezed fields on a symmetric beam splitter. The resultant beams exhibit strong quantum noise correlations in the dark polarization plane. To verify entanglement generation, we characterized 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 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 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.
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.
Continuous variable polarization states have attracted much attention due to their apparent applicability to quantum information networks. Polarization entanglement was presented by transformation of the well-known quadrature entanglement onto the polarization basis. The inseparability criteria as well as the EPR paradox criteria for Stokes operators were also demonstrated. In this paper the generation of such highly quantum correlated states using the interference of two fiber-based polarization squeezing sources is presented. This squeezing can be efficiently created based on the nonlinear effect experienced by ultra-short pulses in fused silica fibers. Two linearly orthogonal polarized modes with identical amplitudes propagate through a polarization maintaining fiber, they experience the same nonlinearity and the phase of the interference between them is controlled to achieve circularly polarized light at the output.
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 on the generation of a continuous variable Einstein-Podolsky-Rosen (EPR) entanglement using an optical fiber interferometer. The Kerr nonlinearity in the fiber is exploited for the generation of two independent squeezed beams. These interfere at a beam splitter and EPR entanglement is obtained between the output beams. The correlation of the amplitude (phase) quadratures is measured to be 4.0+/-0.2 (4.0+/-0.4) dB below the quantum noise limit. The sum criterion for these squeezing variances 0.80+/-0.03<2 verifies the nonseparability of the state. The product of the inferred uncertainties for one beam (0.64+/-0.08) is well below the EPR limit of unity.