Possibility of Atom Entanglement through Fish-Eye Lens

Nearly 150 years ago, physicist James Maxwell proposed an intriguing concept regarding a circular lens. He suggested that a lens with a thicker center and gradually thinning edges would exhibit fascinating optical behavior. Specifically, when light passes through this lens, it would travel in perfect circles, resulting in unique curved paths of light.

Maxwell also observed that this lens resembled the eye of a fish, at least in a broad sense. This lens configuration, known as Maxwell’s fish-eye lens, has since become a theoretical construct in physics. It should be noted that this theoretical lens differs slightly from commercially available fish-eye lenses used in cameras and telescopes.Recently, scientists from MIT and Harvard University conducted a groundbreaking study on this unique theoretical lens from a quantum mechanical perspective. They aimed to understand how individual atoms and photons would behave within the lens. Their findings, published in Physical Review A, reveal that the fish-eye lens’s distinctive configuration allows it to guide single photons through the lens. This guidance leads to the entanglement of pairs of atoms, even over considerable distances.

Entanglement is a quantum phenomenon where the properties of one particle become linked or correlated with those of another particle, even when separated by vast distances. The team’s research suggests that fish-eye lenses hold promise as a means of entangling atoms and other quantum bits, which are essential components for developing quantum computers.The first author of the study, Janos Perczel, a graduate student in MIT’s Department of Physics, explains, “We discovered that the fish-eye lens possesses a unique quality that no other two-dimensional device possesses. It can maintain the ability to entangle particles over large distances, not just for two atoms, but for multiple pairs of atoms that are far apart. The ability to entangle and connect these various quantum bits is crucial in advancing quantum mechanics and exploring its applications.”

The team’s findings also revealed that the fish-eye lens, in contrast to recent assertions, does not yield an impeccable image. Scientists have previously speculated that Maxwell’s fish-eye lens could potentially serve as a “perfect lens” – a lens capable of surpassing the diffraction limit, thereby enabling the focusing of light to a point smaller than its own wavelength. This ideal imaging, according to scientific predictions, should result in an image with virtually boundless resolution and exceptional clarity.

However, through the utilization of a simulated fish-eye lens and the examination of photon behavior at the quantum level, Perczel and his colleagues determined that it is incapable of producing a flawless image as initially anticipated.

“This discovery indicates that there are certain physical limitations that are exceedingly challenging to overcome,” Perczel remarks. “Even in this particular system, which appeared to be an ideal candidate, these limitations remain intact. It is conceivable that perfect imaging may still be achievable with the fish eye through alternative, more intricate means, but not in the manner originally proposed.”

Perczel’s co-authors on the research paper include Peter Komar and Mikhail Lukin from Harvard University.

A circular path

Maxwell was the first to discover that light can travel in perfect circles within the fish-eye lens due to the varying density of the lens. The density is highest at the center and gradually decreases towards the edges. As light moves slower in denser materials, this explains the optical effect observed when a straw is placed in a glass of water. The water, being denser than the air, causes light to bend and creates the illusion of a disjointed straw.

In the case of the fish-eye lens, the density variations are distributed in a circular pattern, allowing it to curve light and guide it in perfect circles within the lens.

In 2009, Ulf Leonhardt, a physicist at the Weizmann Institute of Science in Israel, studied the optical properties of Maxwell’s fish-eye lens. He observed that when photons are released from a single point source through the lens, the light travels in perfect circles and converges at a single point on the opposite end with minimal loss.According to Perczel, none of the light rays deviate from their intended path. They all follow a precise trajectory and converge at the same spot simultaneously.

Leonhardt briefly mentioned the potential usefulness of the fish-eye lens’ single-point focus in entangling pairs of atoms at opposite ends of the lens. This sparked the interest of Mikhail Lukin, who asked Leonhardt if he had explored this further. Although Leonhardt hadn’t, this conversation led to the initiation of a project to investigate the effectiveness of this entangling operation within the fish-eye lens.

Playing photon ping-pong

The researchers conducted an investigation into the quantum potential of the fish-eye lens by creating a simplified model consisting of two atoms positioned at opposite ends of a two-dimensional fish-eye lens, along with a single photon directed towards the first atom. By utilizing established equations from quantum mechanics, the team monitored the photon’s movement through the lens at various points in time and calculated the evolving state of both atoms and their energy levels.Their findings revealed that when a single photon is directed through the lens, it is momentarily absorbed by one of the atoms located at one end of the lens. Subsequently, the photon travels in a circular path within the lens, reaching the second atom positioned at the exact opposite end. This second atom briefly absorbs the photon before sending it back through the lens, resulting in the light precisely converging back onto the first atom.

According to Perczel, the photon undergoes a back-and-forth motion, resembling a game of ping pong between the atoms. Initially, only one atom possesses the photon, followed by the other atom. However, there exists a point between these two extremes where both atoms share the photon equally. This concept of entanglement, a mind-boggling idea in quantum mechanics, is demonstrated as the photon becomes completely shared between the two atoms.Perczel explains that the fish-eye lens enables the photon to entangle the atoms due to its unique geometry. The lens’s density is distributed in a manner that guides light in a perfectly circular trajectory, allowing even a single photon to repeatedly bounce between two specific points along the circular path.

Perczel further emphasizes that if the photon were to disperse in various directions, entanglement would not occur. However, the fish-eye lens grants precise control over the light rays, resulting in an entangled system that spans long distances. This valuable quantum system can be effectively utilized thanks to the fish-eye lens’s capabilities.Perczel states that the fish-eye lens can be utilized to simultaneously entangle numerous pairs of atoms, which is the reason for its usefulness and potential.

Fishy secrets

In the study of the behavior of photons and atoms within the fish-eye lens, the researchers made an interesting discovery. They found that when light gathered on the opposite side of the lens, it did so within an area larger than the wavelength of the photon’s light. This suggests that the lens is unlikely to produce a perfect image.

According to Perczel, one of the researchers, they were able to determine the size of the spot where the photon is recollected during this exchange. They found that it is comparable to the wavelength of the photon, rather than being smaller. This means that the lens cannot achieve perfect imaging, as it would require focusing on an infinitely sharp spot. Their quantum mechanical calculations confirmed this.

Moving forward, the team aims to collaborate with experimentalists to test the quantum behaviors they observed in their modeling. They have even proposed a method to design a fish-eye lens specifically for quantum entanglement experiments in their paper.Perczel emphasizes that the fish-eye lens still holds many secrets and contains fascinating physics. However, it is now gaining attention in the field of quantum technologies. It appears that this lens could be highly valuable for entangling distant quantum bits, which are essential for constructing any practical quantum computer or quantum information processing device.

This article is republished from PhysORG under a Creative Commons license. Read the original article.