### Double-slit interference of single twisted photons

Photons are excellent information carrier for high-speed and large-capacity information processing as they can be transmitted over a long distance with very low loss and without any known decoherence mechanism in free space. As one of fundamental particles, photons have wave-particle duality demonstrated in double-slit experiment. In this experiment, each photon interferes only with itself due to the quantum uncertainty of which path through the optical apparatus it takes, which associates to a particle-like behavior. The interference pattern, which is the accumulated sum of many single photon interference events, accords to a wave-like behavior.

A special property of photons is their orbital angular momentum (OAM) carried by the vortex beam with a helical wavefront of exp(*ilΦ*), where *l* denotes the helical mode index or the topological charge and *Φ* refers to the azimuthal coordinate that is in the plane transverse to the propagation direction, respectively. The different physical dimensions of light, such as polarization, wavelength, and time, OAM is a new degree of freedom of light and an independent physical dimension that can be utilized to carry independent information channels. In quantum mechanics, the amount of OAM carried by the vortex beam is discrete value of *l?* per photon (*?* is the reduced Planck's constant). In particular, OAM has opened the door for boosting optical and quantum ultrahigh-capacity information processing, due to its theoretically unbounded orthogonality and completeness. But the quantum property of single twisted photons carrying the OAM in double-slit is unclear.

The research group led by Prof. Huitian Wang from Nanjing University and Prof. Yongnan Li from Nankai University studies the fundamental property of the OAM at the single-photon level in the double-slit interference. The research results are published in Chinese Optics Letters, Volume 18, No. 10, 2020 (W. Qi, et al., Double-slit interference of single twisted photons). The interference behavior of single twisted photons carrying OAM in the Young's double-slit has been theoretically described by average photon trajectories (APTs).

The double-slit interference process of twisted photons. The averaged photon trajectories demonstrate the helical particle-like behavior (left) and wave character (right) of twisted photons.

The double-slit interference process of twisted photons. The averaged photon trajectories demonstrate the helical particle-like behavior (left) and wave character (right) of twisted photons.

The uncertainty principle suggests that one may not discuss the definite trajectory of a quantum particle, because any measurement of position irrevocably disturbs the momentum, and vice versa. However, it is permitted to define a set of average trajectories for an ensemble of quantum particles. So the APTs can describe indirectly the particle-like behavior of photons.

The simulations show that the APTs exhibit obvious helical structures, which means that the twisted photon travels slower than the established speed of light. The probability of the end-point of the APTs becomes periodic bent-fringed pattern, which reflects the wave character of twisted photons.

Experimentally, they use the correlated photon pairs generated from nonlinear crystal based on spontaneous down conversion as the single photon source, where the signal photon is modulated to carry OAM and then incident to the double-slit, while the idler photon incident on the single-photon detector produces the electrical signal to trigger the intensified Charge-Coupled Detector (ICCD) camera. The time-gated ICCD camera is used to detect individually the signal photons and to reduce the noise. When an idler photon enters into the path of the heralding single-photon detector, the triggered ICCD camera will only record the event of the signal photon. Under the short exposure time of the ICCD camera, the signals recorded by the ICCD camera are randomly distributed in space, indicating the particle nature of photon propagation in space. As the exposure time increases, the spatial distribution of the events detected by the ICCD camera gradually exhibits a regular bent-fringes pattern, just as the theoretical simulation results. This work provides us a more visual and intuitive method for understanding of quantum behaviors.

The method presented in this work can also be used to explore the microscopic behavior of other quantum particles and the helical particle-like property can be applied to quantum precision measurement with help of more advanced and sensitive quantum detection technology.