A classical to quantum optical network link for orbital angular momentum carrying light

Light with orbital angular momentum (OAM) has great potentials in both classical and quantum optical communications such as enhancing the transmission capacity of a single communication channel because of its unlimited dimensions. Based on OAM conservation in second order nonlinear interaction processes, we create a classical to quantum optical network link in OAM degree of freedoms of light via sum frequency generation (SFG) following by a spontaneous parametric down conversion (SPDC). A coherent OAM-carrying beams at telecom wavelength 1550nm is up-converted to 525.5nm OAM-carrying beams in the first crystal, then up-converted OAM-carrying beam is used to pump a second crystal to generate non-degenerate OAM entangled photon pairs at 795nm and 1550nm. By switching the OAM carries by the classical party, the OAM correlation in the quantum party is shifted. High OAM entanglements in two dimensional subspaces are verified. This primary study enables to build a hybrid optical communication network contains both classical and quantum optical network nodes.

In this article, we report the building of a hybrid optical network by link the classical network and quantum network using OAM degree of freedoms of light beam based on sum frequency generation (SFG) followed by spontaneous parametric down conversion (SPDC) in nonlinear crystals.

Results
The experiment consists of two parts, the first part is efficiently up-conversion of OAM carried light beam based on SFG in an external cavity, the second part is SPDC using the up-converted OAM beams to generate non-degenerate OAM entangled photon pairs (see the simple diagram in the top part of Figure 1). High efficiency frequency conversion of OAM-carried light beams in periodically poled nonlinear crystals has been study in detail by us in refs. [19][20][21][22]. In the present experiment (Figure 1), the external cavity is the same as in ref. [22]. The 1550nm beam's power is 12mW (Toptica prodesign), The state of the generated non-degenerate two photon state correlated in OAM can be expressed as [33] , , To show that the total OAM is conserved in the cascade processes of SFG and SPDC and the OAM information carried by the classical coherent light beams at 1550nm is transferred to the signal and idler photons at 795nma and 1550nm. We perform OAM correlation measurements for different signal and idler OAM. The experimental results for OAM of 0, -1 carried by the 1550nm coherent beam are showed in figure 2. Figure 2(a) is a three dimensional bar chart for signal and idler OAM ranges from -5 to 5 for pump beam's OAM of 0 . Due to misalignment, the coincidences of nearby OAMs are larger than non-adjacent OAMs. The maximum coincidence counts in 10 s are 31475 for signal and idler OAMs of 0, the smallest off-diagonal coincidence counts are about 100. Figure 2(b) is the corresponding coincidence counts for signal and idler OAM sum to 0. We can infer that the spiral bandwidth of this two color source is about 5. To increasing the spiral bandwidth, we can use a bigger beam waist, a shorter crystal length [34,35] or change the phase matching condition by tuning the temperature the crystal [36]. Figure 2(b), (c) are the results for the pump OAM of -1, the coincidence counts when the signal and idler OAMs sum to -1 is much bigger than other uncorrelated cases. All these results are in agreements with equation (1), which imply that the total OAM is conserved in the cascade processes, and the OAM information is flowed from the classical party to the quantum party.
These states are represented by points along the equator. States θ are also called sector states, which have 2l sectors of alternating phases.
To quantify the entanglement, we must demonstrate that correlations between signal and idler are persist for superposition states. To verify this, we detect the photons in sector states defined in equation (2) oriented at different angles A θ and B θ respectively. Based on equation (1) and (2), the coincidence rate for detection one photon in A θ and the other in B θ is given by The high-visibility fringes of the joint probability are the signature of two-dimensional entanglement. Any modal impurities will degrade the quality of entanglement, which will reduce the visibilities of the fringes. By post-selection the state in equation (1) into two-dimensional subspaces, the states can be approximated as The above states are normalized with the chosen subspaces and are entangled in OAM. By changing phase masks on SLMs, entangled states with any given l can be prepared.
The experimental results in two-dimensional subspace of (l=1, 2) respectively. All the visibilities are greater than 71%, which is sufficient to violate CHSH inequality and imply the present of two-dimensional entanglement. Therefore we further characterize the entanglement by measuring the CHSH inequality S parameter [40,41]. The definition of S in our experiment for angles A θ and B θ of the phase masks on the two SLMs are ( , ) ( , ) ( , ) ( , ) The inequality is violated for values of S which are greater than 2. ( , ) A B E θ θ is calculated from the coincidence counts at particular sets of the hologram on the two SLMs, For entanglement state l Φ , the inequality is maximally violated for example when To completely describe an entangled state, reconstruction the density matrix is necessary. To reconstruct the density matrix of l Φ , we follow the quantum tomography methods analogous to two-bit polarization entanglement states [42]. We define L l = and R l = − . At least 16 projection measurements at the projection basis L , R , 1/ 2(

Conclusion and discussion
We have demonstrated a proof of principle experiments for building a link for classical Holograms used in the experiments. We use OAM index of 2 as an example to illustrate the holograms used for each measurement in the experiments. The holograms used are listed in Figure 4.