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The Orbital Angular Momentum of Light with an Azimuthal Backflow

Researchers at the University of Warsaw's Faculty of Physics superposed two clockwise twisted light beams to create anti-clockwise twists in the ensuing superposition's dark regions. The findings of the study were published in the prominent journal “Optica.” This discovery has significance for the study of light-matter interactions and is a step toward observing a strange phenomenon known as quantum backflow.

The Orbital Angular Momentum of Light with an Azimuthal Backflow

The superposition of two light beams with different amplitudes carrying only negative orbital angular momentum (OAM) gives rise to a locally positive OAM in the dark regions. This counterintuitive effect is termed ‘azimuthal backflow.’ (Artwork credits: Anat Daniel, Faculty of Physics, University of Warsaw)

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. When you spin such a ball clockwise, for example, you similarly expect it to keep spinning in the same direction.

Bohnishikha Ghosh, Doctoral Student, Faculty of Physics, University of Warsaw

However, things become more complicated when dealing with particles rather than balls in quantum mechanics.

In classical mechanics, an object has a known position. Meanwhile, in quantum mechanics and optics, an object can be in the so-called superposition, which means that a given particle can be in two or more positions at the same time.

Dr Radek Lapkiewicz, Head, Quantum Imaging Laboratory, Faculty of Physics, University of Warsaw

Quantum particles, like the aforementioned tennis ball, can have the potential to go backwards or spin in the other direction during certain periods of time.

Physicists call such a phenomenon backflow.

Bohnishikha Ghosh, Doctoral Student, University of Warsaw

Backflow in Optics

Thus far, backflow in quantum systems has not been detected experimentally. Rather, it has been effectively accomplished in classical optics by the use of light beams.

The relationship between the anomalous behavior of optical waves at local scales and backflow in quantum mechanics was investigated theoretically by Yakir Aharonov, Michael V. Berry, and Sandu Popescu. Y. Eliezer and colleagues synthesized a complicated wavefront to study optical backflow. Afterward, using the simple interference of two beams, Dr Anat Daniel et al. in Dr. Radek Lapkiewicz's group have shown this effect in one dimension.

Dr Anat Daniel added, “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.

Researchers from the University of Warsaw’s Faculty of Physics have demonstrated the two-dimensional backflow effect in a recent publication titled “Azimuthal backflow in light carrying orbital angular momentum,” which was published in the esteemed magazine Optica.

In our study, we have superposed two beams of light twisted in a clockwise direction and locally observed counterclockwise twists,” explained Dr Lapkiewicz.

The researchers employed a Shack-Hartman wavefront sensor to observe the occurrence. For two-dimensional spatial measurements, the system offers excellent sensitivity. It comprises a microlens array positioned in front of a CMOS (complementary metal-oxide semiconductor) sensor.

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,” added Bernard Gorzkowski, a doctoral student in the Quantum Imaging Laboratory, Faculty of Physics.

It is noteworthy that the first experimental generation of orbital angular momentum-carrying light beams with azimuthal (spiral) phase dependence was achieved in 1993 by Marco Beijersbergen et al. utilizing cylindrical lenses. Since then, they have been used in a wide range of domains, including optical microscopy and optical tweezers, the inventor of which, Arthur Ashkin, was awarded the 2018 Nobel Prize in Physics.

These tools enable extensive manipulation of objects at the micro- and nanoscale. Currently, optical tweezers are being utilized to investigate the mechanical characteristics of DNA strands, cell membranes, and the interactions between cancerous and healthy cells.

When Physicists Play Beethoven

The scientists emphasize that superoscillations in phase can be the interpretation of their current demonstration. The first description of the connection between superoscillations in waves and backflow in quantum mechanics was made in 2010 by University of Bristol physicist professor Michael Berry.

A phenomenon known as superoscillation occurs when a superposition's local oscillation is quicker than its fastest Fourier component. Yakir Aharonov and Sandu Popescu made the initial prediction in 1990 when they found that certain combinations of sine waves result in collective wave zones that wiggle faster than any of the parts.

In his publication “Faster than Fourier,” Michael Berry demonstrated the potential for superoscillation by showing that Beethoven's Ninth Symphony could theoretically be performed by combining only sound waves with frequencies lower than 1 Hertz, which are so low that a human couldn't hear them. However, due to the relatively small wave amplitude in the super-oscillatory zones, this is highly impracticable.

Bohnishikha Ghosh concluded, “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.

Aside from this, the University of Warsaw’s Faculty of Physics group’s publication is a step toward the observation of quantum backflow in two dimensions, which is theoretically found to be more resilient than one-dimensional backflow.

Under the FIRST TEAM project “Spatiotemporal photon correlation measurements for quantum metrology and super-resolution microscopy,” which was co-financed by the European Union under the European Regional Development Fund (POIR.04.04.00-00-3004/17-00), the Foundation for Polish Science provided support for this study.

Journal Reference

Ghosh, B., et al. (2023) Azimuthal backflow in light carrying orbital angular momentum. Optica. doi:10.1364/OPTICA.495710.


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