Fish-Eye Lens May Entangle Pairs of Atoms

Estimated reading time: 7 minutes

To investigate the quantum potential of the fish-eye lens, the researchers modeled the lens as the simplest possible system, consisting of two atoms, one at either end of a two-dimensional fish-eye lens, and a single photon, aimed at the first atom. Using established equations of quantum mechanics, the team tracked the photon at any given point in time as it traveled through the lens, and calculated the state of both atoms and their energy levels through time.

They found that when a single photon is shone through the lens, it is temporarily absorbed by an atom at one end of the lens. It then circles through the lens, to the second atom at the precise opposite end of the lens. This second atom momentarily absorbs the photon before sending it back through the lens, where the light collects precisely back on the first atom.

“The photon is bounced back and forth, and the atoms are basically playing ping pong,” Perczel says. “Initially only one of the atoms has the photon, and then the other one. But between these two extremes, there’s a point where both of them kind of have it. It’s this mind-blowing quantum mechanics idea of entanglement, where the photon is completely shared equally between the two atoms.”

Perczel says that the photon is able to entangle the atoms because of the unique geometry of the fish-eye lens. The lens’ density is distributed in such a way that it guides light in a perfectly circular pattern and can cause even a single photon to bounce back and forth between two precise points along a circular path.

“If the photon just flew away in all directions, there wouldn’t be any entanglement,” Perczel says. “But the fish-eye gives this total control over the light rays, so you have an entangled system over long distances, which is a precious quantum system that you can use.”

As they increased the size of the fish-eye lens in their model, the atoms remained entangled, even over relatively large distances of tens of microns. They also observed that, even if some light escaped the lens, the atoms were able to share enough of a photon’s energy to remain entangled. Finally, as they placed more pairs of atoms in the lens, opposite to one another, along with corresponding photons, these atoms also became simultaneously entangled.

“You can use the fish eye to entangle multiple pairs of atoms at a time, which is what makes it useful and promising,” Perczel says.

Fishy Secrets

In modeling the behavior of photons and atoms in the fish-eye lens, the researchers also found that, as light collected on the opposite end of the lens, it did so within an area that was larger than the wavelength of the photon’s light, meaning that the lens likely cannot produce a perfect image.

“We can precisely ask the question during this photon exchange, what’s the size of the spot to which the photon gets recollected? And we found that it’s comparable to the wavelength of the photon, and not smaller,” Perczel says. “Perfect imaging would imply it would focus on an infinitely sharp spot. However, that is not what our quantum mechanical calculations showed us.”

Going forward, the team hopes to work with experimentalists to test the quantum behaviors they observed in their modeling. In fact, in their paper, the team also briefly proposes a way to design a fish-eye lens for quantum entanglement experiments.

“The fish-eye lens still has its secrets, and remarkable physics buried in it,” Perczel says. “But now it’s making an appearance in quantum technologies where it turns out this lens could be really useful for entangling distant quantum bits, which is the basic building block for building any useful quantum computer or quantum information processing device.”

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