Twisted light transmission over 143 km

Abstract

Spatial modes of light can potentially carry a vast amount of information, making them promising candidates for both classical and quantum communication. However, the distribution of such modes over large distances remains difficult. Intermodal coupling complicates their use with common fibers, whereas free-space transmission is thought to be strongly influenced by atmospheric turbulence. Here, we show the transmission of orbital angular momentum modes of light over a distance of 143 km between two Canary Islands, which is 50× greater than the maximum distance achieved previously. As a demonstration of the transmission quality, we use superpositions of these modes to encode a short message. At the receiver, an artificial neural network is used for distinguishing between the different twisted light superpositions. The algorithm is able to identify different mode superpositions with an accuracy of more than 80% up to the third mode order and decode the transmitted message with an error rate of 8.33%. Using our data, we estimate that the distribution of orbital angular momentum entanglement over more than 100 km of free space is feasible. Moreover, the quality of our free-space link can be further improved by the use of state-of-the-art adaptive optics systems.

Keywords: atmospheric turbulence; high-dimensional states; long-distance communication; orbital angular momentum.

Fig. 1.

(A) Sketch of the experimental setup. The sender is located on the roof of the Jacobus Kapteyn telescope on the island of La Palma and consists of a 60-mW laser with a wavelength of 532 nm modulated by an SLM. Different phase holograms on the SLM encode different spatial modes. The modes are magnified with a sending telescope and sent over 143 km to the receiver at the island of Tenerife. Extra mirrors used in the actual sending setup are not shown for simplicity. The structure of received modes is observed on the wall of the Optical Ground Station telescope owned by the ESA and recorded with a camera. (B) Photo of the sender taken during extremely turbulent conditions on La Palma. (Inset) Small vortices and eddies formed by the water vapor in the air are clearly visible. At the sending lens an ℓ = ±1 can be seen. Modes sent under these conditions were not discernible at the receiver. (C) Long-time exposure photo showing an OAM superposition of ℓ = ±1 being transmitted over the Caldera de Taburiente (silhouetted in black) from La Palma to Tenerife. (Insets) Note that the double-lobed modal structure of the beam is clearly visible. A theoretical plot of the mode superposition cross-section is shown for comparison.

Fig. 2.

(A–D) Examples of OAM mode superpositions received on the wall of the telescope Observatorio del Teide after propagating through 143 km of free space between the islands of La Palma and Tenerife. The diameter of the observatory is roughly 11 m. The lobed modal structure is clearly visible for mode superpositions with ℓ = ±1, ±2, and ±3. Images C and D show the rotation of an ℓ = ±3 mode superposition by π/3 when the relative phase $\alpha$ is changed by π. (E–H) Examples of pure OAM (vortex) modes observed at the receiver. The intensity null at the center of the modes is clearly visible. The mode diameter gets larger as the OAM quantum number ℓ is increased, and is seen to approach the size of the telescope wall for ℓ = 7. The size of the modes clearly increases for higher orders. Note that these images were taken at a time when atmospheric conditions were stable.

Fig. 3.

Cross-talk matrices showing the success probability with which the transmitted OAM mode superpositions were correctly identified at the receiver. (A–C) Results for superpositions of ℓ = ±1, ±2, and ±3 modes with relative phases of $\mathrm{\Delta }\alpha =\pi /4,\hspace{0.17em}\pi /2,\hspace{0.17em}\text{and}\hspace{0.17em}\pi$, respectively. The different relative phases correspond to different rotations of the superposition structure. The received modes were correctly identified by our detection algorithm with an average success probability of 82%. (D) During a turbulent night, eight modes consisting of superpositions of ℓ = ±1 were identified with a success probability of only 22.7%. When we restrict ourselves to a subset of these modes with $\mathrm{\Delta }\alpha =\pi /2$ or $\pi$ (highlighted with red squares and reanalyzed by the neural network each time), the success probability increases significantly (E and F). The ability to resolve all eight of these modes is required for device-independent quantum key distribution (violation of a Bell inequality), four modes are necessary for entanglement-based quantum key distribution (violation of an entanglement witness), and two modes can be used for classical communication with 1 bit per mode.

Fig. 4.

Encoding and decoding of a short message with twisted light superpositions. The message “Hello World!” is sent letter by letter. Every letter is encoded into three ℓ = ±1 superpositions with four different relative phase settings. For example, the letter “H” is encoded as 0, 2, and 0. Thus, every mode corresponds to 2 bits of information. After 143 km of transmission, the modes are recorded and characterized with an artificial neural network. The same alphabet is used to decode the letter from the mode superpositions. The final recorded message is “Hello WorldP.” The last letter is a “P” (which is encoded as 1,0,0) instead of an “!” (which is encoded as 0,0,0). This error is due to one incorrectly detected mode.