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Physical Review Letters

Observation of a nonclassical Berry’s phase for the photon

Paul G. Kwiat, R. Y. Chiao

Published Feb 4, 1991• 176 citations
Publisher

Abstract

Coincidence detection of photon pairs produced in parametric fluorescence, in conjunction with a Michelson interferometer in which one member of each pair acquired a geometrical phase due to a cycle in polarization states, has allowed the first observation of Berry's phase at the single-photon level. We have verified that each interfering photon was essentially in an n=1 Fock state, by means of a beam splitter following the interferometer combined with a triple-coincidence technique. The results can be interpreted in terms of a nonlocal collapse of the wave function.

DOI
10.1103/physrevlett.66.588

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Coincidence detection of photon pairs produced in parametric fluorescence, in conjunction with a Michelson interferometer in which one member of each pair acquired a geometrical phase due to a cycle in polarization states, has allowed the first observation of Berry's phase at the single-photon level. We have verified that each interfering photon was essentially in an n=1 Fock state, by means of a beam splitter following the interferometer combined with a triple-coincidence technique. The results can be interpreted in terms of a nonlocal collapse of the wave function.
Berry's phases in optics have been studied extensively, and examples are typically discussed in quantum-mechanical terms. To our knowledge, however, experimental demonstrations have been performed only at the classical level. We report the first observation of a Berry's phase at the single-photon level. In particular, we investigated Pan-charatnam's phase,1 which is acquired whenever light is taken through a closed cycle of polarization states, e.g., with various retardation plates. Correlated pairs of linearly-polarized photons were produced by parametric fluorescence in a UV-pumped KDP crystal. One of each pair was directed into a photomultiplier tube (PMT1). The other was directed into a Michelson interferometer, one arm of which contained two quarter-wave plates, that was used to generate a Berry's phase.
The wave function of a quantum system may acquire an additional phase factor (the geometric phase), when its parameters undergo a cyclic change. An optical manifestation of the geometric phase is the change in the phase of a light wave produced when its state of polarization is taken around a circuit on the Poincare sphere. This phase change can be verified by interferometric measurements. We describe an interferometer in which the two beams traverse the same path in opposite directions, so that their optical paths are always equal, and the phase difference between them is varied by operating on the geometric phase. Measurements made with this interferometer, at a light level at which the probability of more than one photon being present simultaneously in the interferometer was negligibly small, confirmed that the interference effects observed due to the geometric phase persist down to the single photon level.
Nonlocal effects in quantum mechanics associated with entangled states have been the subject of much recent interest.1,2 Franson1 suggested that one can observe a violation of Bell's inequalities for position and time by use of two spatially separated interferometers. We report on the observation of a closely related two-photon interference. A signal photon at frequency ωs and an idler photon at frequency ωi = ωp – ωs are created simultaneously, i.e., as a conjugate pair, in parametric fluorescence inside a KDP crystal from the annihilation of a single UV pump photon with frequency ωp3.
Photon pairs produced by type-I and type-II parametric down-conversion are passed through a Michelson interferometer. Two quarter-wave plates in one arm of the interferometer allow variation of the polarization state of the photons. We investigate experimentally the geometric phase or Pancharatnam phase acquired by single photons and photon pairs dependent on the solid angle that is subtended by the circuit that represents the varying state of polarization on the Poincar\'e sphere. It is found that the geometric phase acquired by the pair depends on the initial polarization state of the two photons. If both photons are in equal states of linear polarization, we observe a doubling of the geometric phase compared to single photons; in the case of orthogonal states of linear polarization, the geometric phase is completely canceled. Our results show the role of Pancharatnam's phase in nonclassical two-photon interference phenomena and the interplay between the geometric phase and the dynamical phase in these phenomena.
An advanced wave model is applied to a two-photon interference experiment to show that the observed interference effect is due to the geometrical phase of a two-photon state produced in spontaneous parametric down-conversion. The polarization state of the signal-idler pair is changed adiabatically so that the ``loop'' on the Poincar\'e sphere is opened in the signal channel and closed in the idler channel. Therefore, we observed an essentially nonlocal geometrical phase, shared by the entangled photon pair, or a biphoton.