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arXiv:quant-ph/0104139 · Physical Review A

Violation of multiparticle Bell inequalities for low- and high-flux parametric amplification using both vacuum and entangled input states

M. D. Reid, William J. Munro, F. De Martini

Published Sep 4, 2002• 37 citations
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Abstract

We show how polarization measurements on the output fields generated by parametric down conversion will reveal a violation of multiparticle Bell inequalities, in the regime of both low- and high-output intensity. In this case, each spatially separated system, upon which a measurement is performed, is comprised of more than one particle. In view of the formal analogy with spin systems, the proposal provides an opportunity to test the predictions of quantum mechanics for spatially separated higher spin states. Here the quantum behavior possible even where measurements are performed on systems of large quantum (particle) number may be demonstrated. Our proposal applies to both vacuum-state signal and idler inputs, and also to the quantum-injected parametric amplifier as studied by De Martini et al. The effect of detector inefficiencies is included, and weaker Bell-Clauser-Horne inequalities are derived to enable realistic tests of local hidden variables with auxiliary assumptions for the multiparticle situation.

DOI
10.1103/physreva.66.033801

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We show how polarization measurements on the output fields generated by parametric down conversion will reveal a violation of multiparticle Bell inequalities, in the regime of both low- and high-output intensity. In this case, each spatially separated system, upon which a measurement is performed, is comprised of more than one particle. In view of the formal analogy with spin systems, the proposal provides an opportunity to test the predictions of quantum mechanics for spatially separated higher spin states. Here the quantum behavior possible even where measurements are performed on systems of large quantum (particle) number may be demonstrated. Our proposal applies to both vacuum-state signal and idler inputs, and also to the quantum-injected parametric amplifier as studied by De Martini et al. The effect of detector inefficiencies is included, and weaker Bell-Clauser-Horne inequalities are derived to enable realistic tests of local hidden variables with auxiliary assumptions for the multiparticle situation.
We show that various experimental configurations using correlated photon-number states are predicted to violate many forms of Bell's inequality. This test is potentially one of macroscopic quantum mechanics in that violations are predicted for situations where large numbers of photons are detected at a single detector at a time. The configurations also allow higher-spin tests of quantum mechanics. We indicate how the violations of Bell inequalities might be achieved with both parametric amplification and parametric oscillation. The effect of photodetection inefficiencies is analyzed. In order to investigate the potential for Bell-inequality tests in the high-intensity regime of recent experiments where detection efficiencies may be very high, we introduce a simple model for the effect of electronic noise that introduces a poor resolution of the photon number detected.
We show that correlated photon-number states predicted to violate a Bell's inequality of the Clauser-Horne-Shimony-Holt type might be generated from parametric amplification. The test is potentially one of macroscopic quantum mechanics in that violations are predicted for situations where a large number of photons are detected in a single detector at one time. The traditional amplifier and detectors allow violation only for regimes where the probability of generation of a macroscopic state is very small. We suggest that this probability may be dramatically improved with the use of squeezing and photon-number-state-preparation techniques.
We demonstrate the experimental violation of a spin-1 Bell inequality. The spin-1 inequality is based on the Clauser, Horne, Shimony, and Holt formalism. For entangled spin-1 particles, the maximum quantum-mechanical prediction is 2.55 as opposed to a maximum of 2, predicted using local hidden variables. We obtained an experimental value of 2.27+/-0.02 using the four-photon state generated by pulsed, type-II, stimulated parametric down-conversion. This is a violation of the spin-1 Bell inequality by more than 13 standard deviations.
Coincidence detections are measured between the output ports of a beam splitter whose input is an orthogonally polarized two-photon state produced in type-II spontaneous parametric down-conversion. When the delays between the two optical paths leading to each detector are varied by two spatially separated Pockel cells, a two-photon interference effect is seen that highlights a simultaneous entanglement in both spin and space-time variables. In contrast to all previous experimental tests of Bell's in- equalities, which have utilized states entangled with respect to only one type of observable, the double entanglement realized here allows the demonstration of two different types of Bell inequality violations in one experimental setup.
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.