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PSA Proceedings of the Biennial Meeting of the Philosophy of Science Association

Correlations and Physical Locality

Arthur I. Fine

Published Jan 1, 1980• 52 citations
Publisher

Abstract

Correlations between the behavior of pairs of particles are generated in the following experimental situation. An on-line source emits a stream of two-particle systems, where each system is in one and the same quantum state. After emission, the particles – call then (I) and (II) – move off in opposite directions. Each particle then encounters one of several possible barriers that either it passes or doesn't. A short distance behind each barrier is a detector set to register the presence of the particle, should it get that far. Finally, the detectors are connected by a timed relay and counter that registers a “coincidence count” should the two detectors fire within a set, brief time interval. When the experiment is run with various different barriers, detection rates accumulate for each barrier singly, and coincidence rates (the correlations) for the various pairs of barriers.

DOI
10.1086/psaprocbienmeetp.1980.2.192609

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Correlations between the behavior of pairs of particles are generated in the following experimental situation. An on-line source emits a stream of two-particle systems, where each system is in one and the same quantum state. After emission, the particles – call then (I) and (II) – move off in opposite directions. Each particle then encounters one of several possible barriers that either it passes or doesn't. A short distance behind each barrier is a detector set to register the presence of the particle, should it get that far. Finally, the detectors are connected by a timed relay and counter that registers a “coincidence count” should the two detectors fire within a set, brief time interval. When the experiment is run with various different barriers, detection rates accumulate for each barrier singly, and coincidence rates (the correlations) for the various pairs of barriers.
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In this study of quantum optics, we want to extract information associated with quantum mechanically entangled photon pairs. Measurements involved here take advantage of the fact that the photon pairs, created at the same point in space and time, will arrive “in coincidence” at detectors placed equally far from the source. Conservation of momentum also constrains the placement of these detectors. These effects, in combination, allow us to differentiate between these entangled photons and other stray photons that may reach the detectors. Initial efforts have included building a more stable laser mount, studying parametric down conversion (the process of converting the single beam into the entangled photon pairs), and establishing a small time interval for coincidence detection. For this, we explore the consequences of moving away from a Field Programmable Gate Array (FPGA) for coincidence measurements and towards the use of a Programmable System on a Chip (PSoC), which essentially combines the fast digital logic gates of an FPGA with micro-controller functionality. We are gaining hands-on experience with some highly theoretical aspects intrinsic to quantum mechanics, expanding upon laboratory setups described in Mark Beck’s recent text on quantum mechanics, as well as materials from Exploring Quantum Physics through Hands-On Projects by David Prutchi and Shanni R. Prutchi.
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A two-body quantum correlation is calculated for a particle and an infinite potential well in which it is trapped or either a barrier or finite well over which it traverses. Correlated interference results when the incident and reflected particle substates and their associated well or barrier substates overlap. Measurement of the particle in this region causes a splitting of the well or barrier substate at subsequent times. The joint probability density, which is a function both of the different positions and different times at which the particle and well or barrier are measured, is derived assuming that no interaction occurs between the time each is measured.
When a positron/electron pair annihilate via the two-photon pathway, the emitted photons are momentum correlated. This correlation ensures that they move along a straight line path in opposite directions. An experiment performed in 2004 by Dr. V.D. Irby measured the time interval between \ndetection of the photons. He observed a decay in the number of counts with increasing detection time interval, which he described using a Lorentzian, the line width of which at full-width half-maximum is \nmeasured to be 120ps. The data collected by Irby is interesting because current theory predicts that because the source is so localized (the effective source width used by Irby is safely within 5rnrn) the photons should be detected within a time interval of ?t=d/c where d is the thickness of the source. This time interval corresponds to 17ps. This thesis fits the results to an exponential, and shows that this exponentially decaying nature of the coincidence time interval is characteristic of the entanglement of the two photons. We find that the wavefunctions of the photons decoheres in space according to how long the particle pair took to decay (which is exponential), and that the probability of simultaneous \ndetection depends on the exponential of the product of the lifetime of positronium and the detection time interval.