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Physical Review A

Geometric phases in two-photon interference experiments

Jurgen Brendel, Wolfgang Dultz, W. Martienssen

Published Oct 1, 1995• 44 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.52.2551

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Journal of Physics Conference Series•Jan 1, 2011•2 citations
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.
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.
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.
We report the experimental observation of the non-local geometric phase in Hanbury Brown-Twiss polarized intensity interferometry.The experiment involves two independent, polarized, incoherent sources, illuminating two polarized detectors.Varying the relative polarization angle between the detectors introduces a geometric phase equal to half the solid angle on the Poincaré sphere traced out by a pair of single photons.Local measurements at either detector do not reveal the effect of the geometric phase, which appears only in the coincidence counts between the two detectors, showing a genuinely non-local effect.We show experimentally that coincidence rates of photon arrival times at separated detectors can be controlled by the two-photon geometric phase.This effect can be used for manipulating and controlling photonic entanglement.
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 method of obtaining the dynamic and geometric part of the phase introduced by a birefringent medium in two kinds of interferometric experiments is presented. The mathematical formulas for the phases obtained using Jones formalism are visualized with the specific triangles on the Poincaré sphere. Generally, these triangles are similar to those used in the Pancharatnam's original construction developed by Courtial to calculate the Pancharatnam geometric phase for the light passing through a single birefringent plate. In these graphical constructions following Courtial's idea, we used the points representing both of the birefringent medium's eigenvectors. This allowed the most intuitive explanation of the mechanism of dividing the whole phase shift introduced by the birefringent plate into two different parts: dynamical and geometrical. The considered constructions were used as a description of two simple experiments with a birefringent medium in a Mach-Zehnder interferometer and a polariscopic setup. The experimental verifications of our theoretical predictions should convince the reader of the correctness of the assumed model.
We present a novel interferometric arrangement that makes it possible to measure with great versatility geometric phases produced in polarization states of classical light. Our arrangement is robust against thermal and mechanical disturbances and can be set up in a Mach-Zehnder, a Michelson or a Sagnac configuration. We present results concerning the geometric phase as an extension of previous measurements of the Pancharatnam, or total phase. The geometric phase is obtained by compensating the dynamical contribution to the total phase, so as to extract out of it a purely geometric phase. This can be achieved over trajectories on the Poincare sphere that are not necessarily restricted to be great circles (geodesics). We thus demonstrate the feasibility of our method for dynamical extraction of the geometric contribution to the total phase, a prerequisite for building geometric quantum gates. Although our results correspond to polarization states of classical light, the same methodology could be applied in the case of polarization states of single photons.