Observation of a topological edge state among localized bulk states in the anisotropic quantum Rabi model

In the world of quantum physics, scientists often look for special states of matter that are protected by the underlying rules of symmetry. Imagine a material where electricity flows only along the edges, while the inside remains completely still. These "edge states" are robust; they can survive bumps and imperfections that would destroy ordinary currents. This phenomenon, known as topology, usually relies on a repeating pattern, like the regular tiles on a floor, to create these protected paths. However, nature is not always so orderly. In systems where this repeating pattern is broken or missing, the usual way of finding these edge states fails. If the entire system is jumbled, both the edge states and the ordinary states inside the material can get stuck in the same place, making them look identical just by looking at where they are located. The challenge for physicists has been to find a way to tell them apart when they are both trapped in the same spot.

A team of researchers has now solved this puzzle by creating a new kind of quantum system in a laboratory and observing a special edge state that reveals itself through its internal structure rather than its location. Using a quantum simulator built from trapped ions—tiny charged atoms held in place by electric fields—the scientists recreated a model known as the anisotropic quantum Rabi model. In this setup, the atoms act as a synthetic lattice, a grid of points where quantum particles can hop. Unlike a standard grid where the connections between points are all the same, the connections in this experiment get stronger as you move further out, breaking the usual repeating pattern. Despite this disorder, the researchers successfully prepared a specific quantum state that sits at the edge of the system. They found that while this state looked just as stuck in place as the ordinary states around it, it possessed unique internal fingerprints: a distinct handedness and a complete separation between its spin and motion components.

The experiment was conducted using a chain of two ytterbium ions, where one ion served as the main actor and the other as a witness to measure the results. The scientists manipulated the interactions between the ion's internal spin and its physical motion using carefully tuned laser beams. By slowly adjusting the strength of these interactions, they guided the system into a specific energy state. In the topological phase they created, a special zero-energy state emerged. The researchers compared this state to several ordinary states that also existed in the system. When they looked at where the particles were likely to be found, both the special edge state and the ordinary states appeared localized, or stuck, near the beginning of the chain. This confirmed that simply looking at the position of the particles was not enough to distinguish the topological state from the rest.

To find the difference, the team examined the internal properties of the states. They measured a property called chirality, which describes a kind of handedness or directionality in the quantum system. The special edge state showed a very clear, consistent handedness, acting almost entirely as a right-handed state. In contrast, the ordinary bulk states were a messy mix of both left and right, averaging out to no clear direction. Furthermore, the researchers looked at how the spin and the motion of the ion were linked. In the ordinary states, the spin and motion were deeply entangled, meaning the state of one could not be described without the other. However, the special edge state was remarkably clean; its spin and motion were almost completely separate, behaving as if they were two independent objects that just happened to be in the same place.

The investigation went deeper into the motion part of the special state. Using a technique called phase-space tomography, which maps out the quantum state in a way similar to taking a photograph of a wave, the team discovered that the motion component of the edge state was a "squeezed vacuum." This is a highly non-classical state where the uncertainty in one aspect of the motion is reduced below the standard limit, while the uncertainty in the other aspect increases. The researchers measured this squeezing to be as high as 6.45 decibels, a significant amount that confirms the state is far from ordinary. As they increased the strength of the interaction, the squeezing became more pronounced, matching theoretical predictions until the system became too noisy to maintain the perfect state.

These findings demonstrate that even in a system without a repeating pattern, topological edge states can exist and be identified. The key is not to look for where the state is located, but to look at what the state is made of. By identifying the unique handedness and the separation of its parts, the researchers proved that the topological nature of the state survives the disorder. This work establishes a new way to probe topological phenomena, showing that the internal structure of a quantum state can serve as a reliable signature, even when the state is hidden among other localized states. The ability to create and characterize these states in a controlled environment opens the door to exploring more complex topological models and potentially developing new methods for robust quantum information processing.