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arXiv:quant-ph/0410217 · Europhysics Letters (EPL)

Two-photon interference with thermal light

Giuliano Scarcelli, A Valencia, Y Shih

Published Nov 16, 2004• 97 citations
arXivHTMLPDF

Abstract

The study of entangled states has greatly improved the basic understanding about two-photon interferometry. Two-photon interference is not the interference of two photons but the result of superposition among indistinguishable two-photon amplitudes. The concept of two-photon amplitude, however, has generally been restricted to the case of entangled photons. In this letter we report an experimental study that may extend this concept to the general case of independent photons. The experiment also shows interesting practical applications regarding the possibility of obtaining high-resolution interference patterns with thermal sources.

DOI
10.1209/epl/i2004-10280-8

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The study of entangled states has greatly improved the basic understanding about two-photon interferometry. Two-photon interference is not the interference of two photons but the result of superposition among indistinguishable two-photon amplitudes. The concept of two-photon amplitude, however, has generally been restricted to the case of entangled photons. In this letter we report an experimental study that may extend this concept to the general case of independent photons. The experiment also shows interesting practical applications regarding the possibility of obtaining high-resolution interference patterns with thermal sources.
The study of entangled states greatly advanced our understanding about two-photon interferometry. Two-photon interference is not the interference between two photons, it is about a pair of photons interfering with the pair itself. In the language of quantum theory, two-photon interference is the result of superposition between different yet indistinguishable two-photon probability amplitudes. Under certain conditions, the observed second-order interference can be factorized into a product of two individual classic first-order interferences. In this case, the interference is not only observable from the intensity fluctuation correlation measurement, or from the photon number fluctuation correlation measurement, of two photodetectors, but also observable in the counting rate of each individual photodetector. It may not be uneasy to accept the quantum concept of two-photon interference for “classical” thermal radiation. Indeed, the radiation Planck dealt with was “classical” thermal light. Perhaps, no one would even expect observing nontrivial second-order correlation from a laser beam, since laser field is non-Gaussin.
Wereport anexperiment that extends theconcept oftwo-photon probability ampli- tudetothegeneral caseofindependent photons. Theexperiment also shows interesting practical applications regarding highresolution interference patterns withthermal sources. © 2004Optical Society ofAmerica OCIS codes:(270.4180) Multiphoton processes, (000.1600) Classical andQuantum physics Thesuperposition principle isprobably themostmysterious andfascinating concept ofthetheory ofquan- tummechanics (1). Quantumtheory ofthesecond order interferometry describes thephysical process of ajoint photo-electron eventatspace-time points (r1, tl) and(r2, t2), produced bytwolight quanta with distinguishable and/or indistinguishable alternative amplitudes (2). Besides probing thefundamental issues ofquantum theory, themassive study ofentangled states hasprovided great insights ontwo-photon in- terferometry (3). Inparticular, wehaveabetter understandiilg ofthetroubling statement ofDirac: Each photon interferes onlywithitself. Interference betweeil twodifferent photons neveroccurs.' Thequestion whether twoindividual photons canorcannot interfere witheachother hasbeenanswered experimentally based onthestudy oftwo-photon interferometry ofSPDC:two-photon interference cannot simply bede- scribed intermsofinterference oftwoindependent photons butmustbeenvisioned asanactual two-photon phenomenon inwhich theindistinguishable alternatives aretwo-photon amplitudes cointributing tothefinal joint photo-electron events (4). Theconcept oftwo-photon amplitude issomehow troublinig, probably because ofthenonlocality thatitimplies, andso,ifaccepted, ithasgenerally beenconsidered peculiar ofentangled photons.
We present experimental observations of a nonclassic and nonlocal interference effect with frequency-entangled photon pairs. We observed two-photon interference in a Hong–Ou–Mandel interferometer by monitoring the coincidence-counting rate as we varied the path-length difference or the relative time delay between two photons. The quantum-mechanical probabilities of joint detection by two detectors that respond to different frequency components exhibit differences that depend not only on the arrangement of the detector pairs but on the spectral filtering. The experimental results provide more understanding of two-photon entanglement and of the interference effects that arise from superposition of indistinguishable probability amplitudes.
Superposition and indistinguishablility between probability amplitudes have played an essential role in observing quantum interference effects of correlated photons. The Hong-Ou-Mandel interference and interferences of the path-entangled photon number state are of special interest in the field of quantum information technologies. However, a fully generalized two-photon quantum interferometric scheme accounting for the Hong-Ou-Mandel scheme and path-entangled photon number states has not yet been proposed. Here we report the experimental demonstrations of the generalized two-photon interferometry with both the interferometric properties of the Hong-Ou-Mandel effect and the fully unfolded version of the path-entangled photon number state using photon-pair sources, which are independently generated by spontaneous parametric down-conversion. Our experimental scheme explains two-photon interference fringes revealing single- and two-photon coherence properties in a single interferometer setup. Using the proposed interferometric measurement, it is possible to directly estimate the joint spectral intensity of a photon pair source.
We propose an incoherent interferometer which can partly modify the spatial correlation property of thermal light. Applying the interferometer to the two-photon double-slit interference with thermal light, we find that the subwavelength interference patterns appear in the intensity correlation not only between two same polarized photons at different positions but also between two orthogonally polarized photons at the same position. The latter can correspond to the two-photon double-slit interference using a two-photon entangled source. Our experimental result suggests that a thermal light source is capable of accomplishing subwavelength lithography technique to surpass the Rayleigh resolution limit.