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arXiv:quant-ph/9907072 · Physical Review A

Spin-correlated interferometry for polarized and unpolarized photons on a beam splitter

Mladen Pavičić

Published Oct 1, 1994• 21 citations
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Abstract

Spin-correlated interferometry of the fourth order for independent polarized as well as unpolarized photons arriving simultaneously at a beam splitter and exhibiting spin correlation while leaving it is formulated and discussed in the quantum approach. The beam splitter is recognized as a source of genuine singlet photon states. Also, typical nonclassical beating between photons taking part in the interference of the fourth order is given a polarization-dependent explanation.

DOI
10.1103/physreva.50.3486

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Spin-correlated interferometry of the fourth order for independent polarized as well as unpolarized photons arriving simultaneously at a beam splitter and exhibiting spin correlation while leaving it is formulated and discussed in the quantum approach. The beam splitter is recognized as a source of genuine singlet photon states. Also, typical nonclassical beating between photons taking part in the interference of the fourth order is given a polarization-dependent explanation.
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 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 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.
The interference of two single photons impinging on a beam splitter is measured in a time-resolved manner. Using long photons of different frequencies emitted from an atom-cavity system, a quantum beat with a visibility close to 100% is observed in the correlation between the photodetections at the output ports of the beam splitter. The time dependence of the beat amplitude reflects the coherence properties of the photons. Most remarkably, simultaneous photodetections are never observed, so that a temporal filter allows one to obtain perfect two-photon coalescence even for nonperfect photons.
We present our source of polarization entangled photons, which consist of orthogonally polarized and collinear parametric down converted photons sent to the same input of a nonpolarizing beam splitter. We show that a too straightforward characterization of the quantum state cannot account for all the experimental observations, in particular for the behavior of the doublecounts, which are the coincidences produced whenever both photons are dispatched by the beam splitter to the same measuring station (either Alice or Bob). We argue that in order to account for all observations, the state has to be entangled in polarization before the non-polarizing beam splitter, and we discuss the intriguing and nevertheless essential role of the time-compensation required to obtain such a polarization entanglement.
The quantum Rayleigh spontaneous emission replaces entangled photons with independent ones in homogeneous dielectric media where single photons cannot propagate in a straight line. Single and independent groups of photons, described by the original bare states of Jaynes-Cummings model, deliver the correct expectation values for the number of photons carried by a photonic wavefront, its complex optical field, and phase quadratures. The intrinsic longitudinal field profile associated with a photonic wavefront is derived for any instantaneous number of photons. These photonic properties enable a step-by-step analysis of various beam splitters and interferometric filters. As a result, generalized expressions are derived for the correlation functions characterizing counting of coincident numbers of photons for fourth-order interference, whether classical or quantum optical, without entangled photons.