Multipath Entanglement of Two Photons

We present a novel optical device based on an integrated system of microlenses and single-mode optical fibers. It allows us to collect and direct into many modes two photons generated by spontaneous parametric down-conversion. By this device multiqubit entangled states and/or multilevel qudit states of two photons, encoded in the longitudinal momentum degree of freedom, are created. The multipath photon entanglement realized by this device is expected to find important applications in modern quantum information technology.

Figure 1

(a) Labeling of the correlated pairs of SPDC modes. Photon $A$ ($B$) can be collected with equal probability into one of the four modes $|1{⟩}_j$, $|2{⟩}_j$, $|3{⟩}_j$, or $|4{⟩}_j$ ($j=A,B$), which are relabeled as shown in (b). (b) Scheme needed for measurement of photon $A$. Here the left ($\ell$) and right ($r$) modes interfere on beam splitters ${\mathrm{BS}}_1$ and ${\mathrm{BS}}_1^{\prime }$, while further interference occurs on ${\mathrm{BS}}_2$ between the external ($E$) and internal ($I$) modes. An identical scheme is needed for photon $B$. (c) Experimental setup: The GL-SMF integrated system injects photon pairs emitted by the crystal into the chained interferometer. The path of photon $A$ ($B$) is indicated by the continuous red (dashed blue) line. By this scheme, ${\mathrm{BS}}_1$ plays simultaneously the role of ${\mathrm{BS}}_1$ and ${\mathrm{BS}}_1^{\prime }$ on side (b) for both photons. The internal and external modes coming out of the right side of ${\mathrm{BS}}_1$ interfere on the beam splitter ${\mathrm{BS}}_2$. Photon $A$ and photon $B$ are separately detected by two single photon counting modules. Micrometric translation stages allow variation of path delays $\Delta x_1,\dots ,\Delta x_3$. Wave plates $\lambda /4$ and $\lambda /2$ enable polarization restoration of photons after SMF transmission. Inset: Picture of the 8 GL-SMF system.

Figure 2

Interference patterns obtained by spatial superposition of the (a) internal and (b) external modes on ${\mathrm{BS}}_1$ as a function of delays $\Delta x_1$ and $\Delta x_3$. (c) “Hybrid” interference condition obtained, varying $\Delta x_2$, by spatial superposition on ${\mathrm{BS}}_2$ of internal and external modes. Each solid (red) line has been drawn by using the value of visibility measured at $\Delta x_i=0$ (see text).

Figure 3

Coincidence count oscillations demonstrating multipath entanglement. The first two traces correspond to interference occurring on ${\mathrm{BS}}_1$ of internal and external modes, separately. The third trace refers to the whole set of mode pairs when no interference occurs on ${\mathrm{BS}}_2$ (i.e., for $\Delta x_1=\Delta x_3=0$ and $\Delta x_2\ne 0$). Here the upper (660) and lower (135) bound are given by the sum of maxima and minima, respectively, of the first two traces. In the last trace, coincidences are measured in conditions of complete mode interference ($\Delta x_1=\Delta x_2=\Delta x_3=0$).