Fiber Transport of Spatially Entangled Photons

Entanglement in the spatial degrees of freedom of photons is an interesting resource for quantum information. For practical distribution of such entangled photons, it is desirable to use an optical fiber, which in this case has to support multiple transverse modes. Here we report the use of a hollow-core photonic crystal fiber to transport spatially entangled qubits.

Figure 1

(a) Experimental setup. (b) Electron micrograph of the cross section of the HC PCF. The core diameter is $25\mu \mathrm{m}$, which results in an half opening angle of the fundamental mode of 44 mrad. The inset shows a near-field optical image (same scale) of the core area, acquired by using incoherent ($800\pm 10\mathrm{nm}$) illumination; this shows approximately circular mode confinement.

Figure 2

Fiber transport of 2D spatially entangled photons in the degenerate case (i.e., superpositions of the $|{\mathrm{HG}}_{1,0}⟩$ and $|{\mathrm{HG}}_{0,1}⟩$ states). Both mode analyzers are equipped with a step phase plate which can be rotated. To obtain a coincidence fringe, plate $A$ is rotated, while plate $B$ is kept fixed. No significant fringe is detected in the single-detector count rates.

Figure 3

Parameter scan of the Clauser-Horne-Shimony-Holt $S$ parameter as a function of $({\beta }_1,{\beta }_2)$ for fixed $({\alpha }_1,{\alpha }_2)$. Each pixel shows color-coded $S({\alpha }_1=0°,{\alpha }_2=-45°,{\beta }_1,{\beta }_2)$, which is calculated by using 16 different coincidence count measurements at different orientations of the phase plates. Regions where the Clauser-Horne-Shimony-Holt inequality ($S\le 2$) is violated are colored white.

Figure 4

Fiber transport of nondegenerate superpositions of photon modes. Analyzer $A$ projects on a superposition of $|{\mathrm{HG}}_{0,0}⟩$ and $|{\mathrm{HG}}_{1,0}⟩$; analyzer $B$ (Gaussian probe) scans normal to the phase plate step of analyzer $A$. The dip in coincidence counts (arrow) is directly proportional to the phase plate displacement ${\Delta }_{\mathrm{PP},A}$. The experimental coincidence count rate is normalized to the single-detector count rate, and the theoretical curves (through lines) are scaled vertically with the same constant to match the data. The visibility of the three curves is 76%, 74%, and 55%, respectively (from top to bottom). We define the visibility here as $(\max -\min )/(\max +\min )$, where max is the average of the count rates in the two peaks that are adjacent to the dip and min is the count rate in the dip.