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arXiv:1110.0416 · Europhysics Letters (EPL)

Non-local geometric phase in two-photon interferometry

Anthony Martin, Olivier Alibart, Jean-Christophe Flesch, Joseph Samuel, Supurna Sinha, Sébastien Tanzilli, Anders Kastberg

Published Jan 1, 2012• 7 citations
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Abstract

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.

DOI
10.1209/0295-5075/97/10003

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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.
We propose a polarized intensity interferometry experiment, which measures the nonlocal Pancharatnam phase acquired by a pair of Hanbury-Brown--Twiss photons. The setup involves two polarized thermal sources illuminating two polarized detectors. Varying the relative polarization angle of the detectors introduces a two-photon geometric phase. Local measurements at either detector do not reveal the effects of the phase, which is an optical analog of the multiparticle Aharonov-Bohm effect. The geometric phase sheds light on the three-slit experiment and suggests ways of tuning entanglement.
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.
We demonstrate the existence of a non-local geometric phase in the intensity-intensity correlations of classical incoherent light, that is not seen in the lower-order correlations. This two-photon Pancharatnam phase was observed and modulated in a Mach-Zehnder interferometer. Using acousto-optic interaction, independent phase noise was introduced to light in the two arms of the interferometer to create two independent incoherent classical sources from laser light. The experiment is the classical optical analogue of the multi-particle Aharonov-Bohm effect. As the trajectory of light over the Poincaré sphere introduces a phase shift observable only in the intensity-intensity correlation, it provides a means of deflecting the two-photon wavefront, while having no effect on single photons.
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.
Quantum entanglement enables a wide range of fundamental studies and practical applications in quantum optics, computing, and communication. In this work, we investigate two-photon interference using position-momentum entangled photons generated via Type-II Spontaneous Parametric Down-Conversion (SPDC). By employing a double-slit setup, we explore two distinct quantum interference phenomena: the Hanbury Brown and Twiss (HBT) effect, where the photons pass through different slits, and NOON-state interference, where both photons traverse the same slit. We deterministically separate the two photons based on their orthogonal polarizations and demonstrate that both interference effects persist despite their distinguishability at the detectors. This result goes beyond the conventional understanding of two-photon interference and reveals a novel nonlocal HBT effect, where interference occurs even in the absence of spatial overlap, and is rooted in entanglement. Our findings deepen the understanding of quantum interference and open new avenues for applications in quantum optics and precision measurement.
The geometric phase, originating from the cyclic evolution of a state, such as polarization on the Poincaré sphere, is typically measured through interferometric approaches that often include unwanted contributions from the dynamic phase. Here, we present a non-interferometric technique based on quantum correlation of pair photons to measure the geometric phase of a classical beam. The transfer of geometric phase of the classical pump beam arising from the cyclic evolution of its polarization state on the Poincaré sphere onto the polarization-entangled pair photons generated via spontaneous parametric down-conversion in a Sagnac interferometer enables easy control over the quantum state. Characterization of the generated quantum states reveals that the geometric phase of the pump beam controls the coincidence counts, entanglement visibility, Bell's parameter, quantum state tomography, and fidelity in close agreement with theoretical predictions. We observe sinusoidal modulation of the Bell's parameter and state fidelity with changes in the geometric phase, resulting in transitions between orthogonal Bell states and Bell-like maximally entangled states. Our results establish the geometric phase of the classical pump as a tunable parameter for quantum state control, offering a compact, passive platform for phase manipulation in quantum photonic systems, enabling geometric phase-based quantum gates, and compensating unwanted phase acquired by the quantum state on propagation.