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Frontiers in Optics

Nonclassical Interferometry with a Single-Photon Interferometer

Enrique J. Galvez, Mehul Malik, B. C. Melius

Published Jan 1, 2006• 0 citations
Publisher

Abstract

We present experiments that use quantum-state correlations between polarization-entangled photon pairs to specify the phase and amplitude of an interference pattern remotely. Photons produced by parametric down conversion are sent to an interferometer while the entangled partners are sent to a phase shifter. By manipulating the quantum state of the light we were able specify the phase and amplitude of the interference pattern with the settings of optical elements in the path of the light that does not go through the interferometer. The results are in excellent agreement with the predictions.

DOI
10.1364/fio.2006.jwd113

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We prepared polarization-entangled photon pairs and sent one of the photons through a Mach-Zehnder interferometer. The apparatus was arranged so that when going through each arm of the interferometer the pairs were in a different Bell state. The distinguishability of the interferometer paths was determined by projecting the entangled state of the two photons with a polarizer placed in the path of the photon that does not go through the interferometer. As a consequence, actions on the remote photon determined nonlocally the visibility of the interference pattern. We present a full theoretical analysis and experimental results that confirm the theoretical predictions.
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.
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We consider Mach-Zehnder and Hong-Ou-Mandel interferometers with nonclassical states of light as input, and study the effect that dispersion inside the interferometer has on the sensitivity of phase measurements. We study in detail a number of different one- and two-photon input states, including Fock, dual Fock, maximally path-entangled $\ensuremath{\mid}N,0⟩+⟨{0}_{,}N\ensuremath{\mid}$ (``N00N'') states, and photon pairs from parametric down-conversion. Assuming there is a phase shift ${\ensuremath{\phi}}_{0}$ in one arm of the interferometer, we compute the probabilities of measurement outcomes as a function of ${\ensuremath{\phi}}_{0}$, and then compute the Shannon mutual information between ${\ensuremath{\phi}}_{0}$ and the measurements. This provides a means of quantitatively comparing the utility of various input states for determining the phase in the presence of dispersion. In addition, we consider a simplified model of parametric down-conversion for which probabilities can be explicitly computed analytically, and which serves as a limiting case of the more realistic down-conversion model.