Quantum motility-induced phase separation

In the bustling world of physics, there is a class of materials known as active matter. Unlike a pile of sand or a cup of water, which sit still unless pushed from the outside, active matter is made of tiny particles that move on their own. These particles, which can be bacteria, synthetic robots, or even flocks of birds, constantly consume energy to propel themselves forward. When enough of these self-driven particles gather, they do not just move randomly; they organize. One of the most striking ways they organize is through a phenomenon called motility-induced phase separation. Imagine a crowded room where everyone is trying to walk in a specific direction. If the crowd gets too thick, people slow down because they bump into each other. This slowing down causes even more people to pile up behind them, creating a dense, slow-moving cluster, while the areas with fewer people remain fast and empty. This happens even if the particles do not attract each other; the mere act of moving and getting stuck is enough to split the system into dense and dilute regions.

For a long time, this behavior was understood only in the classical world of everyday objects. However, scientists have recently begun asking what happens when these rules are applied to the quantum world, where particles can exist in multiple states at once and are linked by invisible threads of coherence. The question was whether the chaotic, energy-consuming motion of active matter could coexist with the delicate, synchronized nature of quantum mechanics. Would the constant jostling and dissipation of energy destroy the quantum connections, or could the two forces work together to create something entirely new?

A team of researchers has now provided compelling evidence that the answer is yes. By building a theoretical model of active particles that behave according to quantum laws, they have shown that a quantum version of this clustering phenomenon can indeed occur. The researchers created a simulation of a one-dimensional line of particles that act like hard-core bosons, a type of quantum particle that cannot occupy the same space as another. These particles have an internal state, like a tiny arrow pointing left or right, which dictates the direction they move. They hop forward in the direction of their arrow, but they can only land on an empty spot. Occasionally, a quantum process flips their arrow, changing their direction, much like a runner deciding to turn around.

The team ran these simulations using a powerful computational method that allowed them to track the behavior of up to one thousand particles. They found that when the quantum flipping of the arrows happened slowly, the particles began to clump together. Just like in the classical version, the particles slowed down in dense areas, leading to a buildup of matter. However, the results revealed a crucial difference. In the simplest version of their model, the particles formed clusters, but these clusters remained finite in size, never growing to fill the entire line. This is known as microphase separation, where the system organizes into many small, distinct groups rather than one giant mass. The researchers observed that the number of particles in a small section of the line fluctuated wildly, a signature of this clustering behavior.

To see if they could force the particles to separate into a single, massive domain, the researchers added a new rule: a repulsive force between neighbors. This force made it energetically unfavorable for particles to sit next to each other unless they were oriented in a specific way that encouraged them to trap themselves together. With this addition, the simulations showed that the clusters grew dramatically larger as the system size increased, suggesting a true, genuine phase separation where the particles split into a dense region and a dilute region.

Perhaps the most surprising discovery was what happened to the quantum nature of the particles during this chaotic clustering. In classical physics, when particles crash into each other and slow down, any delicate quantum connections are usually destroyed by the noise and friction. The researchers expected the constant hopping and dissipation to wipe out the quantum coherence. Instead, they found that the clustered steady states retained a strong, long-distance quantum coherence. The particles within the dense clusters remained linked in a synchronized quantum state, a feature that has no equivalent in the classical world. The very act of clustering created a protected environment where the quantum connections could survive and even thrive.

The study suggests that the interplay between the energy-consuming drive of active matter and the delicate nature of quantum coherence does not lead to destruction, but to cooperation. The activity that drives the particles to cluster actually helps preserve their quantum state. This finding establishes a new type of nonequilibrium quantum state, distinct from anything seen before. While these results come from computer simulations, the ingredients used to build the model—directed dissipation, coherent rotation, and strict exclusion rules—are within the reach of current experimental technology using ultracold atoms. This opens the door for future experiments to observe these quantum clusters in a real laboratory, potentially revealing a new frontier where the chaotic motion of active matter and the mysterious order of quantum mechanics combine to shape the future of quantum materials.