Researchers at the University of Warsaw's Faculty of Physics have superposed two light beams twisted in the clockwise direction to create anti-clockwise twists in the dark regions of the resultant superposition. This discovery has implications for the study of light-matter interactions and represents a step towards the observation of a quantum backflow.

“Imagine that you are throwing a tennis ball. The ball starts moving forward with positive momentum. If the ball doesn’t hit an obstacle, you are unlikely to expect it to suddenly change direction and come back to you like a boomerang,” notes Bohnishikha Ghosh from University of Warsaw. “When you spin such a ball clockwise, for example, you similarly expect it to keep spinning in the same direction”. “In classical mechanics, an object has a known position. Meanwhile, in quantum mechanics and optics, an object can be in the super­position, which means that a given particle can be in two or more positions at the same time” explains Radek Lapkiewicz from the Quantum Imaging Laboratory. So, quantum particles can behave in quite the opposite way to the aforementioned tennis ball – they may have a probability to move backwards or spin in the opposite direction during some periods of time. “Physicists call such a phenomenon backflow," Bohnishikha Ghosh specifies. 

Backflow in quantum systems has not been experi­mentally observed so far. Instead, it has been success­fully achieved in classical optics, using beams of light. Theoretical works of Yakir Aharonov, Michael V. Berry and Sandu Popescu explored the relation between backflow in quantum mechanics and the anomalous behavior of optical waves in local scales. Y. Eliezer et al. observed optical backflow by synthesi­zing a complex wavefront. Subsequently, in Radek Lapkiewicz's group, Anat Daniel an colleagues have demonstrated this phenomenon in one dimension using the simple interference of two beams. “What I find fascinating about this work is that you realize very easily how things are getting weird when you enter the kingdom of local scale measurements”, says Anat Daniel.

Now, the researchers have shown the backflow effect in two dimensions. “In our study, we have superposed two beams of light twisted in a clockwise direction and locally observed counter­clockwise twists,” explains Lapkiewicz. To observe the phenomenon, the researchers used a Shack-Hartman wavefront sensor. The system, which consists of a microlens array placed in front of a CMOS sensor, provides high sensitivity for two dimensional spatial measurements. “We investi­gated the superposition of two beams carrying only negative orbital angular momentum and observed, in the dark region of the inter­ference pattern, positive local orbital angular momentum. This is the azimuthal backflow,” says Bernard Gorzkowski, a doctoral student in the Quantum Imaging Laboratory.

It is worth mentioning that light beams with azimuthal phase dependence that carry orbital angular momentum were first generated by Marco Beijers­bergen et al. experimentally in 1993 using cylindrical lenses. Since then, they have found applications in many fields, such as optical microscopy or optical tweezers, a tool that allows comprehensive mani­pulation of objects at the micro- and nanoscale. Optical tweezers are currently being used to study the mechanical properties of cell membranes or DNA strands or the interactions between healthy and cancer cells.

As the scientists emphasize, their current demon­stration can be interpreted as super­oscillations in phase. Superoscillation is a phenomenon that refers to situations where the local oscillation of a superposition is faster than its fastest Fourier component. It was first predicted in 1990 by Yakir Aharonov and Sandu Popescu, who discovered that special combinations of sine waves produce regions of the collective wave that wiggle faster than any of the constituents. Michael Berry illustrated the power of super­oscillation by showing that in principle it’s possible to play Beethoven’s Ninth Symphony by combining only sound waves with frequencies below 1 Hertz – frequencies so low that they wouldn’t be heard by a human. This is, however, highly impractical because the amplitude of waves in the super-oscillatory regions is very small.

“The backflow we presented is a manifestation of rapid changes in phase, which could be of importance in appli­cations that involve light–matter interactions such as optical trapping or designing ultra-precise atomic clocks,” says Bohnishikha Ghosh. Apart from these, it is a step in the direction of observing quantum backflow in two dimensions, which has been theoretically found to be more robust than one-dimensional backflow. (Source: U. Warsaw)

Reference: B. Ghosh et al.: Azimuthal backflow in light carrying orbital angular momentum, Optica 10, 1217 (2023); DOI: 10.1364/OPTICA.495710

Link: Quantum Imaging Lab, University of Warsaw, Warsaw, Poland