Orbital Angular Momentum-Entanglement Frequency Transducer

Entanglement is a vital resource for realizing many tasks such as teleportation, secure key distribution, metrology, and quantum computations. To effectively build entanglement between different quantum systems and share information between them, a frequency transducer to convert between quantum states of different wavelengths while retaining its quantum features is indispensable. Information encoded in the photon’s orbital angular momentum (OAM) degrees of freedom is preferred in harnessing the information-carrying capacity of a single photon because of its unlimited dimensions. A quantum transducer, which operates at wavelengths from 1558.3 to 525 nm for OAM qubits, OAM-polarization hybrid-entangled states, and OAM-entangled states, is reported for the first time. Nonclassical properties and entanglements are demonstrated following the conversion process by performing quantum tomography, interference, and Bell inequality measurements. Our results demonstrate the capability to create an entanglement link between different quantum systems operating in a photon’s OAM degrees of freedom, which will be of great importance in building a high-capacity OAM quantum network.

Figure 1

Schematic of the experimental setup. The Sagnac loop is operated in a single circulation direction to generate degenerate orthogonally polarized photon pairs at 1558.3 nm. The mode converter can be used to encode arbitrary qubit states or for converting entanglement type from polarization to OAM. The frequency conversion is performed in a ring cavity, which is pumped at 791.0 nm. The mode detection for idler (signal) photon is performed using SLM $A$ ($B$) (HOLOEYE, LETO, $1920\times 1080$ resolution; SLM $A$, $8\text{−}\mu \mathrm{m}$ pixel pitch, and SLM $B$, $6.4\text{−}\mu \mathrm{m}$ pixel pitch). The frequency up-converted signal photon and idler photon are detected by InGaAs and Si-avalanched single-photon detectors, and subsequently, coincidence measurements are performed (Timeharp 260, Pico Quanta, 1.6-ns coincidence window). CM: cavity mirror; DM: dichromatic mirror.

Figure 2

Reconstructed density matrices for the four qubit states $|R⟩$, $|L⟩$, $|H⟩$, $|D⟩$. The first column shows the intensity and phase distributions imprinted on SLM $A$. The second and third columns give the real and imaginary parts of the density matrices. No background correction is applied.

Figure 3

Two-photon interference fringes for (a) the OAM-polarization hybrid-entangled state and (b) the OAM-entangled state. Uncertainty errors are given assuming a Poisson distribution for the photon statistics. (c),(d) Real and imaginary parts of the reconstructed density matrices for the hybrid-entangled state.