Excitation exchange between identical atoms having arbitrary angular momentum

In the quiet realm of quantum optics, scientists study how light and matter interact at the most fundamental level, focusing on the behavior of individual atoms and the photons they emit or absorb. A central puzzle in this field involves pairs of identical atoms placed near one another. When one atom becomes excited—holding onto a packet of energy—it does not keep that energy to itself for long. Instead, it can pass that energy to its neighbor through the invisible electromagnetic field that surrounds them, a process known as excitation exchange. This interaction is not merely a simple handoff; the atoms can influence each other's internal states in ways that depend on their precise orientation and the geometry of their arrangement. Understanding these exchanges is crucial because it reveals how quantum systems communicate and how energy flows through materials, forming the basis for future technologies that rely on controlling light at the atomic scale.

For decades, researchers have understood how this energy swapping works when the atoms involved have simple structures, specifically when they possess a ground state with no internal angular momentum and an excited state with a single unit of it. In these simpler cases, the rules of the exchange are well-mapped, but they do not tell the whole story for the complex atoms found in nature. Many real-world atoms have more intricate internal structures, with multiple sublevels within their ground and excited states that can hold different amounts of angular momentum. Until now, the mathematical description of how excitation moves between such complex atoms remained incomplete, leaving a gap in our understanding of how these systems behave when they are close together.

A team of researchers at the University of Michigan has now filled this gap by deriving a complete set of equations that describe excitation exchange between two identical atoms with arbitrary angular momentum. Their work moves beyond the simplified models of the past to account for atoms where both the ground and excited states can have any number of internal sublevels. By treating the atoms as having general angular momentum values, the authors were able to calculate exactly how the probability of finding an excitation in one atom or the other evolves over time. They focused on a scenario where the atoms are close enough that the time it takes for light to travel between them is negligible, a condition that holds true for most atomic systems of practical importance. This approach allowed them to isolate the pure effects of the exchange interaction without the complications introduced by the finite speed of light.

The most striking discovery in this new analysis is that the complexity of the atoms' internal structure allows for a phenomenon that is impossible in simpler systems. In the case of atoms with simple structures, the exchange of energy preserves the specific orientation of the atom's internal state; an atom in one specific sublevel can only pass its energy to a neighbor that ends up in the same corresponding sublevel. However, the researchers found that for atoms with more complex angular momentum, the excitation can "swap" between different internal sublevels. This means that an atom in one specific state can transfer its energy to a neighbor, causing that neighbor to end up in a completely different internal state than the one the first atom started in. This swap of internal coherence is a new physical feature that emerges only when the atoms have the necessary complexity, revealing a richer and more dynamic form of interaction than previously imagined.

The authors derived these results by carefully tracking the quantum mechanical amplitudes that describe the state of the two atoms and the surrounding light field. They started with the fundamental laws governing how atoms interact with electric fields and applied a standard approximation that simplifies the math while retaining the essential physics. By solving the resulting equations, they showed how the probability of finding the excitation in either atom changes with time, depending on the distance between the atoms and their orientation relative to each other. Their calculations confirm that while the overall rate at which atoms lose energy to the surrounding space remains consistent with known laws, the way they share energy with each other is far more flexible than previously thought. The work provides a rigorous mathematical framework that predicts exactly how these complex atoms will behave, offering a new tool for physicists who design experiments involving multiple atoms or who seek to control quantum states with high precision.

This research does not claim to have solved every mystery of atomic interaction, nor does it suggest that these effects are easy to observe in every setting. The findings are specific to the theoretical model of two identical atoms in a vacuum, neglecting the delay caused by the speed of light, which is a valid assumption for atoms separated by distances much smaller than the wavelength of the light they emit. The authors emphasize that for most practical atomic systems, this neglect of retardation is justified, making their equations directly applicable to real-world scenarios. The discovery of the swap effect suggests that in experiments with complex atoms, researchers might observe unexpected patterns of energy flow that cannot be explained by older, simpler models. By providing a clear and complete description of these interactions, the paper opens the door to a deeper understanding of how quantum systems communicate, ensuring that future explorations of light and matter are built on a foundation that accounts for the full complexity of the atoms involved.