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Physical Review A

Demonstration of the Einstein-Podolsky-Rosen paradox using nondegenerate parametric amplification

M. D. Reid

Published Jul 1, 1989• 851 citations
Publisher

Abstract

We point out in this paper the possibility of demonstrating the Einstein-Podolsky-Rosen paradox via quadrature phase measurements performed on the two output beams of a nondegenerate parametric amplifier. A technique that might be used to demonstrate the paradox has already been partly developed experimentally.
DOI
10.1103/physreva.40.913

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In this paper the output quadrature phase correlations of a frequency nondegenerate parametric amplifier characterized by asymmetric losses, analysed in a preceding paper are applied to the discussion of the Einstein-Podolsky-Rosen (EPR) paradox. We use the formalism developed by Caves et al to describe the combined field modes and adopt the dual local oscillator homodyning scheme to construct an inferred Heisenberg uncertainty principle. The noise level required to demonstrate the existence of the EPR paradox is calculated and the sensitivity of the EPR inference on the asymmetry of the cavity mirror partial transmittivities and on the detuning in frequency between the two detected output fields is analysed. Such an analysis therefore provides a generalization of previous results reported by Reid and Drummond.
Over the past three decades, numerous demonstrations of the violation of Bell’s inequalities have been reported in optical experiments based upon observations of polarization correlations for photon pairs. Without exception, these measurements as well as those in other systems have involved discrete variables for which the Bell inequalities are applicable. By contrast, an experiment to demonstrate the original proposal by Einstein, Podolsky, and Rosen (EPR)1 for a system of observables with a continuous spectrum has not previously been realized. From many possible theoretical avenues, we have followed the suggestion of Reid and Drummond2 to achieve a demonstration of the EPR paradox for continuous variables by employing a subthreshold optical parametric oscillator (OPO) operated in a frequency-degenerate but polarization-nondegenerate mode.
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.