Two atoms can be made to bounce a single photon with great precision.

Atoms can absorb and re-emit light: this is an everyday phenomenon. However, in most cases, an atom emits a light particle in all possible directions; it is therefore quite difficult to recover this photon.

A research team from TU Wien in Vienna (Austria) has now been able to demonstrate theoretically that by using a special lens it is possible to guarantee that a single photon emitted by one atom will be reabsorbed by a second atom. This second atom not only absorbs the photon, but returns it directly to the first atom. In this way, the atoms transmit the photon to each other with extreme precision, again and again, just like in ping-pong.

How to tame a wave

“If an atom emits a photon somewhere in free space, the direction of emission is completely random. This makes it virtually impossible for another distant atom to capture this photon again,” explains Professor Stefan Rotter from the Institute of theoretical physics from the TU. Vienna. “The photon propagates as a wave, which means that no one can say exactly which direction it is traveling. So it is pure chance whether or not the light particle is reabsorbed by a second atom.”

The situation is different if the experiment is not carried out in a free space but in a closed environment. In acoustics, we know something similar in so-called whisper galleries: if two people place themselves in an elliptical room exactly at the focal points of the ellipse, they hear each other perfectly, even when they do not only whisper in a low voice.

The sound waves are reflected by the elliptical wall so that they end up exactly where the second person is: this person can therefore perfectly hear the quiet whisper.

“In principle, something similar could be constructed for light waves when positioning two atoms at the focal points of an ellipse,” explains Oliver Diekmann, first author of the current publication. “But in practice, the two atoms would have to be positioned very precisely at these focal points.”

The Maxwell fish-eye lens

So the research team developed a better strategy based on the fish-eye lens concept, developed by James Clerk Maxwell, the founder of classical electrodynamics. The lens includes a spatially variable refractive index. While light travels in straight lines in a uniform medium such as air or water, light rays are bent in a Maxwell fish-eye lens.

“In this way, it is possible to ensure that all rays emanating from an atom reach the edge of the lens in a curved path, are then reflected and then arrive at the target atom in another curved path,” explains Oliver Diekmann. In this case, the effect works much more efficiently than in a simple ellipse and deviations from the ideal positions of the atoms are less harmful.

“The light field of this Maxwell fish-eye lens consists of many different oscillation modes. This is reminiscent of playing a musical instrument where different harmonics are generated at the same time,” explains Stefan Rotter. “We were able to show that the coupling between the atom and these different oscillation modes can be adapted in such a way that the photon is transferred from one atom to another with almost certainty, which is quite different from this which would be the case in free space.”

Once the atom has absorbed the photon, it is left in a higher energy state until it re-emits the photon after a very short time. Then the game starts again: the two atoms exchange roles and the photon is returned from the receiving atom to the original emitting atom, and so on.

The effect has been demonstrated theoretically, but practical tests are possible with current technology. “In practice, the efficiency could be further increased by using not just two atoms, but two groups of atoms,” explains Stefan Rotter. “The concept could be an interesting starting point for quantum control systems to study the effects of extremely strong light-matter interaction.”

The work is published in the journal Physical Examination Letters.