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Physical Review Letters

Entangled Quantum Nonlinear Schrödinger Solitons

Yinchieh Lai, Ray‐Kuang Lee

Published Jul 2, 2009• 21 citations
Publisher

Abstract

Considered as a multipartite quantum system, time-multiplexed nonlinear Schrödinger solitons after collision are rigorously proved to become quantum entangled in the sense that their quadrature components of suitably selected internal modes satisfy the inseparability criterion. Clear physical insights for the origin of entanglement are given, and the required homodyne local oscillator pulse shape for optimum entanglement detection is determined.

DOI
10.1103/physrevlett.103.013902

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Considered as a multipartite quantum system, time-multiplexed nonlinear Schrödinger solitons after collision are rigorously proved to become quantum entangled in the sense that their quadrature components of suitably selected internal modes satisfy the inseparability criterion. Clear physical insights for the origin of entanglement are given, and the required homodyne local oscillator pulse shape for optimum entanglement detection is determined.
We have experimentally demonstrated how two beams of light separated by an octave in frequency can become entangled after their interaction in a chi;{(2)} nonlinear medium. The entangler was a nonlinear optical resonator that was strongly driven by coherent light at the fundamental and second-harmonic wavelengths. An interconversion between the fields created quantum correlations in the amplitude and phase quadratures, which were measured by two independent homodyne detectors. Analysis of the resulting correlation matrix revealed a wave function inseparability of 0.74(1)<1, thereby satisfying the criterion of entanglement.
We report an experimental demonstration of the continuous-variable Einstein-Podolsky-Rosen (EPR) paradox and quantum steering using a pulsed light source and nonlinear optical waveguides. In this pulsed light source experiment, time-domain measurements were performed in which one measured value of the quadrature phase amplitude of the light field was independently obtained for each pulse. This independence is useful for application to quantum information processing and fundamental physics. To realize time-domain measurements, in-house built homodyne detectors were used to detect individual pulses. In addition, to improve the temporal-mode matching between the local oscillator (LO) and entangled pulse, the duration of the LO pulse was shortened by single-pass optical parametric amplification. The product of the conditional variances of the quadrature amplitudes was 0.82 ± 0.09 < 1, which satisfies the condition for realization of the EPR paradox and quantum steering.
A general formalism is developed for optimizing homodyne detection of quadrature-noise squeezing by selection of the local-oscillator (LO) field. The optimum LO is the minimum-eigenvalue eigenfunction of a particular Fredholm integral equation whose kernel depends on the signal field's normally ordered and phase-sensitive covariance functions. The squeezing that results from use of the optimum LO equals one plus twice its associated eigenvalue. A continuous-wave (cw) simplification of the general formalism is presented for the case of stationary signal-field covariances when the homodyne photocurrent is spectrum analyzed. Another simplified special case is exhibited for single-spatial-mode operation, such as is encountered in fiber-based quantum-noise experiments. The cw-source–spectrum-analysis approach is used to determine the optimum LO field and its squeezing performance for cw squeezed-state generation in a bulk Kerr medium with a Gaussian spatial-response function. The single-spatial-mode framework is employed to find the optimum LO field and its squeezing performance for pulsed squeezed-state generation in a single-mode optical fiber whose Kerr nonlinearity has a noninstantaneous response function. Comparison of the cw limit of this pulsed analysis with previous cw fiber-squeezing theory reveals a new regime for quadrature-noise reduction: Raman squeezing in fiber four-wave mixing.