Indefinite causal order in cavity quantum electrodynamics

In the quantum world, the rules of cause and effect can become surprisingly fluid. Usually, we think of events happening in a strict sequence: first one thing occurs, then another. If you flip a switch, a light turns on; if you push a ball, it rolls. This linear flow is how our daily lives work, and it is how most quantum experiments are traditionally designed. However, a concept known as indefinite causal order challenges this intuition. It allows for a situation where two events happen, but the question of which one happened first has no definite answer. Instead of a single timeline, the system exists in a superposition of both possible orders simultaneously. While this sounds like a theoretical curiosity, researchers have found that harnessing this ambiguity can offer powerful new tools for processing information, potentially solving problems that are impossible for standard, fixed-order systems.

A team of physicists has now taken this concept out of the realm of light beams and into the domain of atoms and mirrors. In a new study, they explored how indefinite causal order behaves within a cavity quantum electrodynamics system. This is a setup where a single atom interacts with light trapped inside two separate, identical chambers. The researchers wanted to see what would happen if they could make the atom pass through these two chambers in a superposition of both possible orders: going through chamber A then B, and chamber B then A, at the same time. By doing so, they discovered that this strange ordering could create a powerful connection between the light in the two chambers, even though the light waves never touched each other directly.

The experiment involves a single atom, which acts as a messenger, and two empty rooms filled with light. To create the indefinite order, the researchers used a control mechanism, essentially a quantum switch, to decide the atom's path. If the switch is set to one state, the atom travels through the first chamber and then the second. If it is set to the other state, the order is reversed. The breakthrough comes when the switch is placed in a superposition of both states. In this condition, the atom does not choose a single path; it travels through both sequences simultaneously. The researchers found that when the atom emerges from this dual-path journey, the light fields inside the two separate chambers become deeply linked. They share a quantum connection known as entanglement, meaning the state of the light in one chamber is instantly correlated with the light in the other, despite the fact that the light waves in the two chambers never interacted with one another.

This effect is particularly striking because the ability to create this entanglement is independent of whether the atom started in an excited state or a ground state, as well as the time it takes the atom to transit each cavity. However, the specific resulting state of the light and the probability of obtaining it do depend on the atom's initial conditions and the measurement outcomes. Furthermore, the researchers showed that this process can generate specific, highly complex patterns of light. For instance, if the chambers start with no light at all, the process can create a state where a single photon exists in a superposition of being in the first chamber or the second chamber, but never in both or neither. This is a type of state known as a NOON state, which is valuable for ultra-precise measurements. Even more remarkably, the team demonstrated that the system could swap a photon between the two chambers without changing the state of the atom itself. In a standard setup where the atom travels in a fixed order, such a swap without altering the messenger is impossible. The indefinite order allows the atom to act as a bridge that rearranges the light without leaving a trace of its own journey.

The study also revealed how this indefinite order disrupts the natural rhythm of the system. In standard quantum physics, when an atom interacts with light, it often exhibits a predictable, wavelike oscillation in its energy levels, known as Rabi oscillations. The researchers found that when the indefinite causal order is introduced, this smooth, sinusoidal rhythm either vanishes completely or loses its regular shape entirely. The system no longer behaves with the predictable pulse seen in fixed-order scenarios. Instead, the outcome depends on the specific measurement of the control switch, leading to a variety of possible final states for the light.

The implications of these findings suggest a new way to control the interaction between matter and light. By manipulating the order of events, scientists can create entangled states between distant systems that would otherwise remain separate. The researchers propose that this could be physically realized using a trapped atom moving along a circular path, where the atom's wave packet is split and recombined, effectively allowing it to visit two cavities in a superposition of orders. While the current work is a theoretical investigation based on established models of light-matter interaction, it opens a door to new possibilities. It suggests that by embracing the ambiguity of "which happened first," we can unlock new capabilities for controlling quantum systems, creating entanglement, and performing tasks that are strictly forbidden in a world of fixed cause and effect.