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American Journal of Physics

A hands-on introduction to single photons and quantum mechanics for undergraduates

Brett J. Pearson, David P. Jackson

Published Apr 14, 2010• 76 citations
Publisher

Abstract

We describe a series of experiments used in a sophomore-level quantum physics course that are designed to provide students with a hands-on introduction to quantum mechanics. By measuring correlations, we demonstrate that a helium-neon laser produces results consistent with a classical model of light. We then demonstrate that a light source derived from a spontaneous parametric down-conversion process produces results that can only be described using a quantum theory of light, thus providing a (nearly) single-photon source. These single photons are then sent into a Mach–Zehnder interferometer, and interference fringes are observed whenever the path of the photons cannot be determined. These experiments are investigated theoretically using straightforward quantum-mechanical calculations.

DOI
10.1119/1.3354986

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We describe a series of experiments used in a sophomore-level quantum physics course that are designed to provide students with a hands-on introduction to quantum mechanics. By measuring correlations, we demonstrate that a helium-neon laser produces results consistent with a classical model of light. We then demonstrate that a light source derived from a spontaneous parametric down-conversion process produces results that can only be described using a quantum theory of light, thus providing a (nearly) single-photon source. These single photons are then sent into a Mach–Zehnder interferometer, and interference fringes are observed whenever the path of the photons cannot be determined. These experiments are investigated theoretically using straightforward quantum-mechanical calculations.
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We have developed a series of undergraduate teaching laboratories that explore some of the fundamentals of quantum mechanics. All of the experiments involve performing measurements on individual photons or entangled-photon pairs. The experiments include: "Proving" that light consists of photons, single-photon interference, and tests of local realism. We will describe the experiments, placing an emphasis on an experiment which measures the quantum-mechanical polarization state of a photon. This experiment explicitly demonstrates that measurements performed on one member of an entangled-photon pair effect the results of measurements of the other photon. We will also describe how we have integrated the experiments with our upper-level undergraduate quantum mechanics course.
We describe five quantum mechanics experiments that have been designed for an undergraduate setting. The experiments use correlated photons produced by parametric down conversion to generate interference patterns in interferometers. The photons are counted individually. The experimental results illustrate the consequences of multiple paths, indistinguishability, and entanglement. We analyze the results quantitatively using plane-wave probability amplitudes combined according to Feynman’s rules, the state-vector formalism, and amplitude packets. The apparatus fits on a 2′×4′ optical breadboard.
Over the past several decades, single photon-based path interference in double-slit experiment has been well demonstrated for the particle nature of photons satisfying complementarity theory, where the quantum mechanical interpretation of the single photon interference fringe is given by Born rule for complex amplitudes in measurements. Unlike most conventional methods using entangled photon pairs, here, a classical coherent light source is directly applied for the proof of the same self-interference phenomenon. Instead of double slits, we use a Mach-Zehnder interferometer as usual, where the resulting self-interference fringe of coherent single photons is exactly the same as that of the coherent photon ensemble of the laser, demonstrating that the classical coherence based on the wave nature is rooted in the single photon self-interference. This unexpected result seems to contradict our common understanding of decoherence phenomena caused by multi-wave interference among bandwidth distributed photons in coherence optics.
Abstract The superposition states, allowed by quantum theory, are dramatically diverse with respect to classical states and represent the true quantum states. By using a Mach-Zehnder interferometer we experimentally show how a single photon in a polarization superposition state can produce interference. The experimental setup includes a strongly attenuated laser source, polarizing beam splitters, half-waveplates, polarizers and single-photon detectors. The experimental activity has been performed with high-school students and teachers in several different contexts.
We have performed a series of experiments using a spontaneous parametric down-conversion source to produce pairs of photons in either entangled or non-entangled polarization states. We determine the full quantum mechanical polarization state of one photon, conditioned on the results of measurements performed on the other photon. For non-entangled states, we find that the measured state of one photon is independent of measurements performed on the other. However, for entangled states, the measured state does depend on the results of measurements performed on the other photon. This is possible because of the nonlocal nature of entangled states. These experiments are suitable for an undergraduate teaching laboratory.