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Nearly 150 years ago, the physicist James Maxwell proposed that a circular lens that is thickest at its center, and that gradually thins out at its edges, should exhibit some fascinating optical behavior. Namely, when light is shone through such a lens, it should travel around in perfect circles, creating highly unusual, curved paths of light.
Image Caption: James Maxwell was the first to realize that light is able to travel in perfect circles within the fish-eye lens because the density of the lens changes, with material being thickest at the middle and gradually thinning out toward the edges.
He also noted that such a lens, at least broadly speaking, resembles the eye of a fish. The lens configuration he devised has since been known in physics as Maxwell’s fish-eye lens — a theoretical construct that is only slightly similar to commercially available fish-eye lenses for cameras and telescopes.
Now scientists at MIT and Harvard University have for the first time studied this unique, theoretical lens from a quantum mechanical perspective, to see how individual atoms and photons may behave within the lens. In a study published Wednesday in Physical Review A, they report that the unique configuration of the fish-eye lens enables it to guide single photons through the lens, in such a way as to entangle pairs of atoms, even over relatively long distances.
Entanglement is a quantum phenomenon in which the properties of one particle are linked, or correlated, with those of another particle, even over vast distances. The team’s findings suggest that fish-eye lenses may be a promising vehicle for entangling atoms and other quantum bits, which are the necessary building blocks for designing quantum computers.
“We found that the fish-eye lens has something that no other two-dimensional device has, which is maintaining this entangling ability over large distances, not just for two atoms, but for multiple pairs of distant atoms,” says first author Janos Perczel, a graduate student in MIT’s Department of Physics. “Entanglement and connecting these various quantum bits can be really the name of the game in making a push forward and trying to find applications of quantum mechanics.”
The team also found that the fish-eye lens, contrary to recent claims, does not produce a perfect image. Scientists have thought that Maxwell’s fish-eye may be a candidate for a “perfect lens” — a lens that can go beyond the diffraction limit, meaning that it can focus light to a point that is smaller than the light’s own wavelength. This perfect imaging, scientist predict, should produce an image with essentially unlimited resolution and extreme clarity.
However, by modeling the behavior of photons through a simulated fish-eye lens, at the quantum level, Perczel and his colleagues concluded that it cannot produce a perfect image, as originally predicted.
“This tells you that there are these limits in physics that are really difficult to break,” Perczel says. “Even in this system, which seemed to be a perfect candidate, this limit seems to be obeyed. Perhaps perfect imaging may still be possible with the fish eye in some other, more complicated way, but not as originally proposed.”
A Circular Path
Maxwell was the first to realize that light is able to travel in perfect circles within the fish-eye lens because the density of the lens changes, with material being thickest at the middle and gradually thinning out toward the edges. The denser a material, the slower light moves through it. This explains the optical effect when a straw is placed in a glass half full of water. Because the water is so much denser than the air above it, light suddenly moves more slowly, bending as it travels through water and creating an image that looks as if the straw is disjointed.
In the theoretical fish-eye lens, the differences in density are much more gradual and are distributed in a circular pattern, in such a way that it curves rather bends light, guiding light in perfect circles within the lens.
In 2009, Ulf Leonhardt, a physicist at the Weizmann Institute of Science in Israel was studying the optical properties of Maxwell’s fish-eye lens and observed that, when photons are released through the lens from a single point source, the light travels in perfect circles through the lens and collects at a single point at the opposite end, with very little loss of light.
“None of the light rays wander off in unwanted directions,” Perczel says. “Everything follows a perfect trajectory, and all the light will meet at the same time at the same spot.”
Leonhardt, in reporting his results, made a brief mention as to whether the fish-eye lens’ single-point focus might be useful in precisely entangling pairs of atoms at opposite ends of the lens.
“Mikhail asked him whether he had worked out the answer, and he said he hadn’t,” Perczel says. “That’s how we started this project and started digging deeper into how well this entangling operation works within the fish-eye lens.”