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Physical Review A

Optimizing the photon pair collection efficiency: A step toward a loophole-free Bell’s inequalities experiment

Carlos Henrique Monken, P. H. Souto Ribeiro, Sebastião Pádua

Published Apr 1, 1998• 51 citations
Publisher

Abstract

We show that the photon pair collection efficiency in coincidence measurements can be maximized when the two-photon state is generated in the process of spontaneous parametric down-conversion in a thin crystal. This effect can be used to close part of the so-called detection loophole in Bell's inequalities experiments. The effect is also demonstrated experimentally.

DOI
10.1103/physreva.57.r2267

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We show that the photon pair collection efficiency in coincidence measurements can be maximized when the two-photon state is generated in the process of spontaneous parametric down-conversion in a thin crystal. This effect can be used to close part of the so-called detection loophole in Bell's inequalities experiments. The effect is also demonstrated experimentally.
The importance of photon pair generation can never be overemphasized. It has formed the basis of most fundamental quantum optical experiments like Bell-experiments, quantum teleportation and entanglement swapping. However for considerable number of years Quantum Mechanics in general has remained largely theoretical and within the four corners of laboratories. Quantum Key Distribution is one of the first quantum applications to break this barrier. It provides us with unconditionally secured communication by providing us with efficient alternative to classical cryptography. This study forms part of the effort in realizing efficient way of generating photon pairs through the Spontaneous Parametric Down-Conversion process using a nonlinear crystal cut for type-I phase matching. After generating the photon pairs, the paper examined how they can be detected efficiently. We measured the rate of single photon generation (up to 200 kHz) as well as the rate at which they are detected in coincidence (150 coincidences per second). We further investigated a quantum interference effect (the Hong-Ou-Mandel effect) which classical wave theory has failed to describe. This effect has numerous applications in scalable quantum networks and in linear quantum computing. Finally, a remarkable conversion efficiency of 2.2
A method for preparing a loophole-free four-photon Bell experiments which requires a detection efficiency of 67% is proposed. It enables realistic detection efficiencies of 75% at a visibility of 85%. Two type-II crystals each down convert one correlated photon pair and we entangle one photon from one pair with one photon from the other pair on a highly transparent beam splitter. The entanglement selects two other conjugate photons into a Bell state. Wide solid angles for the conjugate photons then enable us to collect close to 100% of them. The cases when both photon pairs come from only one of the two crystals are successfully taken into account. Hardy's equalities are discussed.
The proof of Nature's nonlocality through Bell-type experiments is a topic of longstanding interest. Nevertheless, no experiments performed thus far have avoided the so-called 'detection loophole,' arising from low detector efficiencies and angular-correlation difficulties. In fact, most, if not all, of the systems employed to date can never close this loophole, even with perfect detectors. In addition, another loophole involving the non-rapid, non-random switching of various parameter settings exists in all past experiments. We discuss a proposal for a potentially loophole-free Bell's inequality experiment. The source of the EPR-correlated pairs consists of two simultaneously-pumped type-2 phase-matched nonlinear crystals and a polarizing beam splitter. The feasibility of such a scheme with current detector technology seems high, and will be discussed. We also present a single-crystal version, motivated by other work presented at this conference. In a separate experiment, we have measured the absolute detection efficiency and time response of four single-photon detectors. The highest observed efficiencies were 70.7 plus or minus 1.9 percent (at 633 nm, with a device from Rockwell International) and 76.4 plus or minus 2.3 percent (at 702 nm, with an EG&G counting module). Possible efficiencies as high as 90 percent were implied. The EG&G devices displayed sub-nanosecond time resolution.
The nonlocality inherent in quantum mechanics has been tested experimentally, but the nonlocal interpretation of all the relevant experiments can be challenged. All past tests of Bell's inequalities have required supplementary assumptions, without which the experimental results satisfy the inequalities, in agreement with the notion of local realism. There are basically three loopholes that need to be closed; neither the cascade sources nor the parametric down-conversion sources of correlation photons used to date are capable of closing all of them, even if the detectors used had been 100% efficient. We propose a two-crystal down-conversion source, relying on type-II collinear phase matching, which should permit a violation of Bell's inequalities without the need for supplementary assumptions. As the source can produce a true singletlike state, it is also relevant for quantum cryptographic applications.
Detecting non-locality requires almost ideal experimental conditions - ideal sources for entangled photon pairs and ideal detectors. Deviations from this ideal situation may critically hamper interpretations of experiments attempting to prove non-locality. Of two major known loopholes, the detector loophole is not yet unequivocally closed. Now another loophole emerges: When in such experiments down converting crystals with lasers as primary sources are used, exceeding threshold values in the Bell inequalities, i.e. their violation, can be caused by so far not fully recognized problems in the generation and detection of photon pairs. Taken together, nonlocality is still not yet unequivocally proven.