Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Two-photon geometrical phase

Dmitry Strekalov, Yanhua H. Shih

Published Oct 1, 1997• 17 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.56.3129

Related papers

Geometric phases in two-photon interference experiments

Jurgen Brendel, Wolfgang Dultz, W. Martienssen

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.

Physical Review A•Oct 1, 1995•44 citations

Polarization entanglement in a crystal with threefold symmetry

E. R. Eliel, Jorrit Visser, Gerard Nienhuis

Summary form only given. The vast majority of experimental studies of entanglement is based on the use of a polarization entangled photon pair or multiples thereof. Typically, such pairs are produced by the process of spontaneous parametric down conversion in a crystal that exhibits a nonzero second-order nonlinear susceptibility and is cut for type II phase matching. These photons are orthogonally polarized along directions imposed by the symmetry, cut and orientation of the nonlinear crystal. Polarization-entangled pairs are then selected by spatial, and possibly spectral, filtering of the down-converted light. When the crystal is pumped with linearly polarized light a rather intuitive picture arises. If one selects the polarization of the signal photon to be linear, the idler photon will also be linearly polarized in such a way that /spl alpha//sub p/ = -(/spl alpha//sub s/ + /spl alpha//sub i/). Here /spl alpha//sub p,s,i/ refer to the polarization directions of pump, signal and idler, respectively. Their polarization state can be characterized by points on the equator of the Poincare sphere. If, for linear polarized pump, the signal is selected to be elliptically polarized, the idler will also be elliptically polarized. On the Poincare sphere signal and idler have equal latitude (on the same hemisphere), while their longitude is determined by the same relation as above. In all cases signal and idler are maximally entangled.

Quantum Electronics and Laser Science Conference•Jun 25, 2003•0 citations

First-order interference of nonclassical light emitted spontaneously at different times

Yoon-Ho Kim, Maria V. Chekhova, S. P. Kulik +2 more

We study the first-order interference in spontaneous parametric down-conversion generated by two pump pulses that are well distinguishable in time. The observed modulation in the angular distribution of the signal photon can only be explained in terms of a quantum-mechanical description based on biphoton states. The condition for observing interference in the signal channel is shown to depend on the parameters of the idler photon.

arXiv:quant-ph/9911014•Physical Review A•Apr 14, 2000•19 citations

The geometric phase in optics: observations at the classical and quantum limits

P. Hariharan

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.

16th Congress of the International Commission for Optics: Optics as a Key to High Technology•Jul 26, 1993•0 citations

Quantum interference with beamlike type-II spontaneous parametric down-conversion

Yoon-Ho Kim

We implement experimentally methods to generate photon-number--path and polarization entangled photon pairs using ``beamlike'' type-II spontaneous parametric down-conversion, in which the signal-idler photon pairs are emitted as two separate circular beams with small emission angles rather than as two diverging cones.

arXiv:quant-ph/0304105•Physical Review A•Jul 2, 2003•49 citations

Tracking phase entanglement during propagation of down-converted photons

Rounak Chatterjee, Vikas S. Bhat, Kiran Bajar +1 more

High-dimensional entanglement in the form of transverse spatial correlation between a pair of photons generated via spontaneous parametric downconversion is not only a valuable resource in many academic and real-life applications but also provides access to several intriguing quantum phenomena. One such non-intuitive phenomenon is phase entanglement, in which the biphoton state is correlated in the complex phase of its wavefunction. This state, which emerges during the propagation of the biphoton wavefunction, exhibits neither position nor momentum correlation, yet retains full entanglement. In this work, we experimentally explore this state in two distinct ways. The first is by tracking the vanishing spatial photon number correlation over propagation distances lying in $\left[0,\infty\right)$, folded into a finite range using single-lens imaging. These observations show excellent agreement with our theoretical predictions based on the Double Gaussian (DG) approximation of the biphoton state. The second approach involves performing a two-photon interference experiment using a double slit and this state, which reveals the correlated phase front. We show, both theoretically and experimentally, that the observed two-photon interference structure is markedly different from that produced by position-correlated photons, as confirmed by computing the joint probability distribution of photons (JPD) and related metrics. Such interference using phase-entangled light has not been attempted before and opens avenues for advanced experiments and applications in the field of spatial entanglement.

arXiv:2505.17906•Physical Review Applied•Jul 14, 2025•3 citations
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.
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.
Summary form only given. The vast majority of experimental studies of entanglement is based on the use of a polarization entangled photon pair or multiples thereof. Typically, such pairs are produced by the process of spontaneous parametric down conversion in a crystal that exhibits a nonzero second-order nonlinear susceptibility and is cut for type II phase matching. These photons are orthogonally polarized along directions imposed by the symmetry, cut and orientation of the nonlinear crystal. Polarization-entangled pairs are then selected by spatial, and possibly spectral, filtering of the down-converted light. When the crystal is pumped with linearly polarized light a rather intuitive picture arises. If one selects the polarization of the signal photon to be linear, the idler photon will also be linearly polarized in such a way that /spl alpha//sub p/ = -(/spl alpha//sub s/ + /spl alpha//sub i/). Here /spl alpha//sub p,s,i/ refer to the polarization directions of pump, signal and idler, respectively. Their polarization state can be characterized by points on the equator of the Poincare sphere. If, for linear polarized pump, the signal is selected to be elliptically polarized, the idler will also be elliptically polarized. On the Poincare sphere signal and idler have equal latitude (on the same hemisphere), while their longitude is determined by the same relation as above. In all cases signal and idler are maximally entangled.
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.
High-dimensional entanglement in the form of transverse spatial correlation between a pair of photons generated via spontaneous parametric downconversion is not only a valuable resource in many academic and real-life applications but also provides access to several intriguing quantum phenomena. One such non-intuitive phenomenon is phase entanglement, in which the biphoton state is correlated in the complex phase of its wavefunction. This state, which emerges during the propagation of the biphoton wavefunction, exhibits neither position nor momentum correlation, yet retains full entanglement. In this work, we experimentally explore this state in two distinct ways. The first is by tracking the vanishing spatial photon number correlation over propagation distances lying in [0,∞)\left[0,\infty\right)[0,∞), folded into a finite range using single-lens imaging. These observations show excellent agreement with our theoretical predictions based on the Double Gaussian (DG) approximation of the biphoton state. The second approach involves performing a two-photon interference experiment using a double slit and this state, which reveals the correlated phase front. We show, both theoretically and experimentally, that the observed two-photon interference structure is markedly different from that produced by position-correlated photons, as confirmed by computing the joint probability distribution of photons (JPD) and related metrics. Such interference using phase-entangled light has not been attempted before and opens avenues for advanced experiments and applications in the field of spatial entanglement.