Abstract

Over the past three decades, numerous demonstrations of the violation fo 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 Drummond^[2] 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. Realization of the EPR paradox for this system involves the nonclassical correlations of quadrature-phase amplitudes for the orthogonally polarized signal and idler fields, with the quadrature-phase amplitudes playing the roles of canonical position and momentum variables. In our experiment, the two quadrature amplitudes $X_s^{\pm }$ of the signal beam are inferred in turn from measurements of the spatially separated quadrature amplitudes $Y_i^{\pm }$ of the idler beam. The error of this inference is quantified by the variances $V_{\pm }=〈{\left(X_s^{\pm }\mp g{Y}_i^{\pm }\right)}^2〉$, with (+, −) referring to the separate errors for the inference of the two signal quadrature amplitudes from the correlated idler amplitudes and the factor g chosen to minimize V_±. The condition V_± < 1 means that the quadrature amplitudes for the signal beam can be specified from measurements of the idler beam to better than the vacuum-state limit for the signal beam alone. Realization of the EPR paradox requires that V₊V₋ < 1, which is in seeming contradiction with the uncertainty principle for the state of the signal beam according to the logic of EPR. In our measurements with dual homodyne detectors, we have recorded V₊ = (0.87 ± 0.02), V₋ = (0.89 ± 0.03), and hence V₊V₋ = (0.77 ± 0.03), which is comfortably below the limit of unity required for the demonstration of the paradox.

© 1992 IQEC