Angular Two-Photon Interference and Angular Two-Qubit States

Using angular-position–orbital-angular-momentum entangled photons, we study angular two-photon interference in a scheme in which entangled photons are made to pass through apertures in the form of double angular slits, and using this scheme, we demonstrate an entangled two-qubit state that is based on the angular-position correlations of entangled photons. The entanglement of the two-qubit state is quantified in terms of concurrence. These results provide an additional means for preparing entangled quantum states for use in quantum information protocols.

Figure 1

(a) Schematic of the experimental setup (see text for details). (b) An example of the phase pattern impressed on the SLM. (c) Two-photon path diagrams showing the four alternative pathways by which signal and idler photons can pass through the angular slits and be detected in coincidence at detectors $D_s$ and $D_i$.

Figure 2

Measurements of the OAM-mode probabilities with the SLMs set for uniform reflectivity. Measured coincidence counts are given as a function of $l$, the OAM-mode order of the detected signal photon, with $-l$ being the OAM-mode order of the idler photon. The solid dots are the expected values based on the theoretical prediction of Ref. 28 [Eq. (10)]; the solid line through the dots is drawn as a visual guide. The fitting parameters are an overall constant factor and the effective beamwidth of down-converted modes as measured by the detection system.

Figure 3

(a) Measured coincidence detection probabilities ${\rho }_{11}$, ${\rho }_{22}$, ${\rho }_{33}$, and ${\rho }_{44}$. The measured probabilities are shown by blue bars (black in the printed version); the probabilities after correcting for random coincidences are shown by light blue bars (gray in the printed version). (b) Measured coincidence counts (light red, gray in the printed version) as functions of $l_s$ for two different values of $l_i$, with $\alpha =\pi /10$ and $\beta =\pi /4$. The solid dots are theoretical fits obtained from Eq. (6), the solid lines are visual guides, and the dashed lines are measured random coincidences for the 10-ns coincidence detection window.

Figure 4

Measured coincidence counts as a function of $l_s$ for four different values of $\beta$, with $\alpha =\pi /10$ and $l_i=0$. Each plot is an average of 24 different plots, taken with the starting angles of both the signal and idler apertures rotated in steps of 15° from 0° to 360°.