From disorder to order: Flocking birds and ‘spinning’ particles

Physicists have long studied how energy and motion emerge in materials when components interact in new ways. Now, their research explores an even stranger frontier: how energy and order can spontaneously emerge at the quantum scale from non-equilibrium interactions. In a new study, researchers in Japan uncovered a phenomenon they call “quantum active matter” and found it exhibits a kind of flocking behavior driven purely by quantum mechanics and non-Hermitian dynamics. Their results, published in Physical Review Research, reveal how a quantum version of flocking can emerge without any explicit aligning interactions – pushing the boundaries of our understanding of emergent behavior at the smallest scales.

Like its classical counterpart known as “active matter,” quantum active matter consists of many interacting parts that individually consume and dissipate energy. But unlike classical systems, quantum active matter behaves according to the strange rules of quantum mechanics rather than classical Newtonian mechanics. “In classical active matter, you have self-propelled particles like birds flocking together,” explains lead researcher Kazuaki Takasan of the University of Tokyo. “In our quantum system, the ‘particles’ are actually quantum bits that can occupy multiple states simultaneously. And their motion is governed not by classical trajectories but by the complex dynamics of quantum wavefunctions.”

Previous researchers had introduced the concept of quantum active matter theoretically and shown how classical phenomena like motility-induced phase separation could manifest on the quantum scale. But Takasan and his collaborators Kyosuke Adachi and Kyogo Kawaguchi wanted to directly observe emergent behaviors purely driven by quantum non-equilibrium dynamics, without analogy to a classical system. “We wanted to explore strange new states of matter that have no classical counterpart,” says Takasan.

The team developed a theoretical model of one-dimensional “quantum spins” – quantum bits that can point either “up” or “down” – moving in a line and interacting with each other. They introduced two key ingredients not present in classical active matter systems: quantum tunneling between spin states, and asymmetric, spin-dependent hopping between sites driven by dissipation. “Dissipation is usually seen as something that destroys quantum effects,” notes Adachi. “But here we use it constructively to induce new emergent behaviors.”

Simulating the quantum dynamics of this “quantum active spin chain” on a computer, the researchers observed a spontaneous transition to a strange new phase of matter. Even without any explicit alignment interaction between spins, the system spontaneously developed long-range ferromagnetic order – all the spins pointed the same way across the entire chain. “We were surprised to see the chain ‘flock’ together purely from the interplay of quantum tunneling, interactions and dissipation,” says Kawaguchi.

To understand the mechanism, the team proved that the dissipation always increases the energy of quantum states where spins point randomly, while leaving the ferromagnetically aligned state unchanged. They also solved the simplified case of just two interacting spins and found the dissipation induces the spins to tightly bind together into a kind of quantum bound state. “In the paramagnetic phase where spins point randomly, dissipation favors the bound state configuration, driving the system toward ferromagnetic order,” explains Takasan.

The researchers developed a simple mean-field theory accounting for the energy advantage of the two-spin bound state. It qualitatively captured the same ferromagnetic phase transition seen in the full simulations. “Our mean-field theory shows the emergence of long-range order ultimately stems from the short-ranged bound states induced locally by dissipation,” says Adachi. Their work provides some of the first insights into how fluctuations, correlations and collective behavior can spontaneously emerge from quantum nonequilibrium dynamics alone.

The phenomenon of “quantum flocking” uncovered here lies beyond the boundaries of conventional quantum phase transitions because it owes to the complex non-Hermitian nature of the system’s dynamics. As such, it may conform to new types of critical behavior not described by ordinary quantum critical points. The team now hopes to simulate larger systems using tensor network techniques to explore whether the transition remains continuous in the thermodynamic limit, and how critical exponents may differ from standard models.

“It was surprising at first to find that the ordering can appear without elaborate interactions between the agents in the quantum model. It was different from what was expected based on biophysical models”

Kazuaki Takasan

The researchers also note their work points towards possible realizations in programmable quantum simulators using cold atomic gases. Two-component quantum gases and spin-dependent hopping have both been achieved experimentally. “Our theory shows how quantum flocking could in principle be observable using dissipation engineered into an optical lattice potential,” says Takasan. More broadly, he notes their results demonstrate how fine control over nonequilibrium fluctuations at the quantum scale could enable directed self-assembly of complex structures – offering a path to realize new active quantum materials with emergent functions.

With quantum simulation and artificial intelligence accelerating discovery at the ultra-small, scientists continue pushing deeper into uncharted territories where quantum, far-from-equilibrium and collective phenomena intersect. The work of Takasan, Adachi and Kawaguchi shows how strange macroscopic order can self-organize even within idealized quantum systems through the interplay of quantum fluctuations and nonequilibrium processes. Their discovery of quantum flocking suggests a vast, unexplored landscape where synchrony, flocking and other collective behaviors may spontaneously emerge from the noisy dynamics of many quantum components. As quantum engineering advances, such phenomena may one day inform the design of novel quantum technologies with emergent functionality arising from cooperative fluctuations on the tiniest of scales.

Reference(s)

1. Kazuaki Takasan, Kyosuke Adachi, Kyogo Kawaguchi. Activity-induced ferromagnetism in one-dimensional quantum many-body systems. Physical Review Research, 2024; 6 (2) DOI: 10.1103/PhysRevResearch.6.023096

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