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arXiv:quant-ph/9908024 · Journal of the Optical Society of America B

Spin-correlated interferometry with beam splitters: preselection of spin-correlated photons

Mladen Pavičić

Published May 1, 1995• 23 citations
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Abstract

A nonclassical feature of the fourth-order interference at a beam splitter, that genuine photon spin singlets are emitted in predetermined directions even when incident photons are unpolarized, has been used in a proposal for an experiment that imposes a quantum spin correlation on truly independent photons. In the experiment two photons from two such singlets interfere at a beam splitter, and as a result the other two photons—which nowhere interacted and whose paths nowhere crossed—exhibit a 100% correlation in polarization, even when no polarization has been measured in the first two photons. The proposed experiment permits closure of the remaining loopholes in the Bell theorem proof, reveals the quantum nonlocality as a property of selection, and pioneers an experimental procedure for the exact preparation of unequal superposition.

DOI
10.1364/josab.12.000821

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A nonclassical feature of the fourth-order interference at a beam splitter, that genuine photon spin singlets are emitted in predetermined directions even when incident photons are unpolarized, has been used in a proposal for an experiment that imposes a quantum spin correlation on truly independent photons. In the experiment two photons from two such singlets interfere at a beam splitter, and as a result the other two photons—which nowhere interacted and whose paths nowhere crossed—exhibit a 100% correlation in polarization, even when no polarization has been measured in the first two photons. The proposed experiment permits closure of the remaining loopholes in the Bell theorem proof, reveals the quantum nonlocality as a property of selection, and pioneers an experimental procedure for the exact preparation of unequal superposition.
We present an experiment which prepare entanglement between photons that nowhere interacted and whose paths nowhere crossed. The experiment puts together two photons from two (non-maximal) singlet-like photon pairs and make them interfere at an asymmetrical beam splitter. As a result one finds polarization correlations between the other companion photons from the pairs whose paths nowhere crossed each other even when no polarization measurements have been carried out on the former photons. The latter set of photons that nowhere interacted are therefore event-ready prepared by their pair-companion photons. The result reveals nonlocality as a property of selection which can even be a preselection. It also reveals that one can predict spin-correlated behaviour of photons in space and at beam splitters by controlling a no-spin observable. [From the Book of Abstracts as appeared at the Workshop.]
We propose a new experiment employing two independent sources of spin correlated photon pairs. Two photons from different unpolarized sources each pass through a polarizer to a detector. Although their trajectories never mix or cross, they exhibit fourth-order-interference-like correlations when the other two photons interfere on a beam splitter even when the latter two do not pass any polarizers at all. A wave packet calculation shows that the experiment permits a very discriminatory test of hidden variable theories.
The simplest possible photon-number-squeezed states containing only two photons and exhibiting sub-poissonian statistics with the Fano factor approaching 0.5 have been used for a proposal of a loophole-free Bell experiment requiring only 67 percent of detection efficiency. The states are obtained by the fourth order interference first of two downconverted photons at an asymmetrical beam splitter and thereupon of two photons from two independent singlets at an asymmetrical beam splitter. In the latter set-up, the other two photons which nowhere interacted and whose paths never crossed appear entangled in a singlet-like correlated state.
The quantum theory of fourth-order interference of light is presented in a general format and compared with classical wave theory. The conditions under which nonclassical phenomena occur are discussed. In particular, the interference between the quantum field and classical field may give rise to a nonclassical effect. For some special states of light, the interference pattern does not disappear even though one field is much stronger than the other, for which no classical analog exists. Fourth-order effects in the interference between two independent fields are analyzed in detail. It is pointed out that the fourth-order interference between independent fields will not disappear when the integration time of detection is of the order of the reciprocal bandwidth of the two light fields as long as the spectra of the two fields are symmetric around the same center frequency, and for some correlated fields, the interference does not vanish even if the detection time is much larger than the reciprocal bandwidth of the fields. A new type of fourth-order interference experiment involving a beam splitter is proposed in which local realism of the Einstein-Podolsky-Rosen form is violated for quantum mechanics. This general argument is then applied to the interference between two photons generated in the parametric down-conversion process. The possibility of violations of Bell's inequalities in interference experiments is investigated.
Quantum mechanical models of beam splitters1 predict interesting fourth-order interference effects when nonclassical light is used. If indistinguishable one-photon states are simultaneously input into each port of a 50/50 beam splitter, the theory predicts that each output will contain either two photons or none. A naive (particle) theory would predict a mixture of two’s and one’s. The required |1,1〉 photon state can be selected in nondegenerate parametric downconversion experiments by photon-counting coincidence detection. The disappearance of this coincidence after a beam splitter has recently been studied,1-2 and the range of path length differences over which the effect can be seen is related by Fourier transform to the photon bandwidth. In our work the bandwidth is not limited by external filters, and we have developed a theory which relates the measured photon length to the geometry of the apparatus and the detailed phase matching conditions at the parametric crystal. This theory of phase matching viewed through a beam splitter produces some unexpected results when the beam splitter is tilted and when large aperture detectors are considered.