Research advances in observing quantum reflux in two dimensions

Researchers from the Faculty of Physics at the University of Warsaw superimposed two clockwise-twisted beams of light to create counterclockwise twists in the dark regions of the resulting superposition. The research results were published in Optics. This discovery has implications for the study of light-matter interactions and represents a step toward observing a peculiar phenomenon known as quantum reflux.

“Imagine 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 at you like a boomerang,” notes Bohnishikha Ghosh, PhD student at the Faculty of Physics at the University of Warsaw. “When you spin a ball clockwise, for example, you expect it to keep spinning in the same direction.”

However, everything gets complicated when, instead of a ball, we are dealing with particles in quantum mechanics. “In classical mechanics, an object has a known position. Meanwhile, in quantum mechanics and optics, an object can be in so-called superposition, which means that a given particle can be in two or more positions at the same time.” explains Dr. Radek Lapkiewicz, head of the Quantum Imaging Laboratory at the Faculty of Physics at the University of Warsaw.

Quantum particles can behave completely opposite to the tennis ball mentioned above – they can be likely to move backwards or spin in the opposite direction during some periods of time. “Physicists call this phenomenon reflux”, specifies Bohnishikha Ghosh.

Reflow in optics

Reflow in quantum systems has not been observed experimentally until now. Instead, it was successfully achieved in classical optics using beams of light. Theoretical work by Yakir Aharonov, Michael V. Berry and Sandu Popescu explored the relationship between backflow in quantum mechanics and the anomalous behavior of optical waves at local scales.

Y. Eliezer et al. observed optical reflow synthesizing a complex wavefront. Later, in Dr. Radek Lapkiewicz’s group, Dr. Anat Daniel et al. demonstrated this phenomenon in one dimension using the simple interference of two beams.

“What I find fascinating about this work is that you easily see how weird things get when you enter the realm of local-scale measurements,” says Dr. Anat Daniel.

In their paper “Azimuthal backflow in light carrying orbital angular momentum”, researchers from the Faculty of Physics at the University of Warsaw showed the backflow effect in two dimensions. “In our study, we superimposed two clockwise-twisted beams of light and locally observed counter-clockwise twists,” explains Dr.

To observe the phenomenon, the researchers used a Shack-Hartman wavefront sensor. The system, which consists of an array of microlenses placed in front of a CMOS (complementary metal-oxide semiconductor) 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 azimuthal backflow,” says Bernard Gorzkowski, PhD student in the Quantum Imaging Laboratory , Faculty of Physics.

It is worth noting that azimuthal (spiral) phase-dependent light beams carrying orbital angular momentum were first generated by Marco Beijersbergen et al. experimentally in 1993 using cylindrical lenses.

Since then, they have found applications in various fields, such as optical microscopy or optical tweezers, a tool that allows the comprehensive manipulation of micro- and nanoscale objects, whose creator, Arthur Ashkin, was honored with the 2018 Nobel Prize in Physics. Optical tweezers are currently being used to study the mechanical properties of cell membranes or DNA strands or the interactions between healthy and cancerous cells.

When physicists play Beethoven

As the scientists emphasize, their current demonstration can be interpreted as in-phase superoscillations. The link between backflow in quantum mechanics and superoscillations in waves was first described in 2010 by Professor Michael Berry, a physicist at the University of Bristol.

Superoscillation is a phenomenon that refers to situations in which 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 move faster than any of the constituents.

Michael Berry, in his publication “Faster than Fourier”, illustrated the power of superoscillation by showing that, in principle, it is possible to play Beethoven’s Ninth Symphony by combining only sound waves with frequencies below 1 Hertz – frequencies so low that they would not be reproduced. be heard by a human. This is, however, highly impractical because the amplitude of the waves in the superoscillatory regions is very small.

“The reflow we present is a manifestation of rapid phase changes, which could be important in applications involving light-matter interactions, such as optical trapping or designing ultra-precise atomic clocks,” says Bohnishikha Ghosh. Furthermore, the publication by the group from the Faculty of Physics at the University of Warsaw is a step towards the observation of quantum reflow in two dimensions, which theoretically turned out to be more robust than one-dimensional reflow.