Quantum entanglement of complex photon polarization patterns in vector beams

Rapid Communication

Quantum entanglement of complex photon polarization patterns in vector beams

Robert Fickler, Radek Lapkiewicz, Sven Ramelow, and Anton Zeilinger

Phys. Rev. A 89, 060301(R) – Published 11 June 2014

Abstract

We report the efficient creation and detection of hybrid entanglement between one photon's polarization and another photon's complex transverse polarization pattern including various polarization singularities. The polarization measurement of the first photon triggers a polarization-sensitive imaging of its partner photon, the vector photon, using a single-photon-sensitive camera. Thereby, the vector photon's complex polarization pattern is reconstructed tomographically dependent on the type of polarization measurement performed on its partner. To evaluate the quality of the observed patterns, we introduce a fidelity-like measure which compares the reconstructed polarization with the theoretically expected one at every transverse spatial position. We find that the measured polarization patterns and the theory overlap by more than 90%. Moreover, we visualize the varying strengths of polarization entanglement for different transverse regions and demonstrate an interesting phenomenon: Each vector photon can be both entangled and not entangled in polarization with its partner photon. We give an intuitive, information-theoretical explanation for our results. Our results pave the way to study quantum properties of the rich field of such complex light modes with the potential to improve various applications in quantum informational tasks.

Received 2 December 2013
Revised 14 April 2014

DOI:https://doi.org/10.1103/PhysRevA.89.060301

Authors & Affiliations

Robert Fickler, Radek Lapkiewicz, Sven Ramelow^*, and Anton Zeilinger

Vienna Center for Quantum Science and Technology, Faculty of Physics, University of Vienna, Boltzmanngasse 5, Vienna A-1090, Austria and Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, Vienna A-1090, Austria

^*Present address: Cornell University, 271 Clark Hall, 142 Science Dr., Ithaca, NY 14853.

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 89, Iss. 6 — June 2014

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Sketch of the experimental setup. Polarization entanglement between two photons is created (green box) in a down-conversion process. One photon is coupled to a single-mode fiber (SMF), delayed by 35 m and brought to the interferometric transfer setup. (a) Here, the path is coherently split according to polarization and the photon state is transferred by a spatial light modulator (SLM) to a different transverse spatial mode for each path. The vector photon state results by recombining the two modes. A removable quarter-wave plate (QWP) rotates the linear polarization components to circular ones in the case of LG and Poincaré vector photon creation. (b) The polarization measurement of the unchanged photon (QWP, polarizer, single-photon detector) is used to trigger an intensified CCD camera (ICCD). For each trigger polarization a spatially resolved polarization tomography of the vector photon is performed (QWP, polarizer, ICCD) and used to reconstruct its complex polarization pattern.
Reuse & Permissions
Figure 2
Transverse polarization tomography from coincidence images. The exemplary measurements were done with diagonally polarized trigger photons and vector photons composed of circularly polarized, first order LG modes $l = + 1$ and $l = - 1$ . (a) Left: The recorded intensity distribution (accumulating single photons for 15 s) depends on the polarization settings in front of the ICCD camera (white letters: H, V, D, A, R, L for horizontal, vertical, diagonal, antidiagonal, and left- and right-hand circular, respectively). Right: Local polarization tomography ( $10 \times 10$ pixel arrays) results in the reconstructed pattern of a cylindrical vector photon (every third vector is shown), more precisely an azimuthally polarized state. The sizes of the polarization vectors correspond to the average intensity which is shown in the background. The colors depict the type and handedness of polarization (blue: linear; red: right elliptical; green: left elliptical). Insets show theoretical intensities and the resulting polarization pattern. (b) Point-to-point overlap between the measured and theoretical polarization. The “local” fidelities are calculated for regions where more than 100 photons have been detected and range from 78% to 99%. The average value of $92.2 \pm 0.1 %$ is given as a quality measure [Eq. (2)].
Reuse & Permissions
Figure 3
Polarization patterns measured for different vector photons entangled with polarized partner photons. The average registered intensity distribution for each trigger polarization (black letters) is shown and overlaid with the measured polarization pattern (every third polarization shown; color coding as in Fig. 2). The average point-by-point fidelity [see main text, Eq. (2) and Fig. 2] is written in white. For H or V polarized trigger photons the polarization is uniformly distributed over the spatial mode. The imprinted phases are presented by gray scale insets (lower left; linearly from 0 = black to 2 $π$ = white). If the trigger photon is found in a superposition of H and V (columns three to six), the vector photon shows different polarization patterns (theoretical pattern on the lower right). Cylindrical vector beam patterns, including radial, azimuthal, and spiral configurations, can be found for HG and LG vector photons. In the third row, patterns of Poincaré photons are shown which exhibit a $C$ -point singularity in the center and a circular $L$ -line singularity around it (dashed circle). Similar $C$ points and $L$ lines can be found in patterns of the custom-tailored Poincaré photon (dashed line).
Reuse & Permissions
Figure 4
Polarization entanglement of the created hybrid entanglement biphoton state. (a) Three different tests for polarization entanglement were performed: witness [red, Eq. (3)], steering [pink, Eq. (4)], and Bell-CHSH [blue, Eq. (5)]. For LG vector photons and Poincaré photons the Bell-CHSH inequality was tested with L, R, D, and A polarization triggers instead of the usual H, V, D, and A polarization settings. The different strengths of the criteria are directly visible in the size of the entanglement regions, i.e., regions with more than 100 photons and an exceeding of the classical bound by at least three standard deviations (Poissonian count statistics assumed). (b) If the polarization setting in front of the ICCD camera is altered (rotation of the reference frame or polarizer) an interesting entanglement pattern appears. Only where the modal overlap of the two components is big enough (and enough photons were detected) can entanglement in polarization be revealed (small insets: theory). (c) Similarly for custom-tailored Poincaré photons, the modal overlap is too small on the left and right parts of the beam irrespectively of the trigger polarization settings (left and right; insets show theory), thus no entanglement is found there.
Reuse & Permissions

Physical Review A

covering atomic, molecular, and optical physics and quantum information