A speed limit for spreading of coherence

Scientists at the Cavendish Laboratory have discovered a fundamental speed limit for how coherence spreads when a Bose–Einstein condensate begins to form. This finding deepens our understanding of how long-range order emerges in quantum matter and could have profound implications for quantum technologies and beyond.

“These results are exciting because they help us understand one of the most basic and broadly relevant questions about quantum matter”

Christoph Eigen

A Bose–Einstein condensate (BEC) is a state of matter that occurs when a group of bosons (particles that can share the same quantum state) are cooled to ultracold temperatures of around a billionth of a degree above absolute zero. In this state, matter behaves coherently, forming a unified macroscopic object where the individual particles move in lockstep.

Discoveries that reveal fundamental speed limits in physical processes often reshape our understanding of physics, such as the speed-of-light limit on how fast information can spread. In the current study, published in Nature, scientists have identified such a limit in a key process: the formation of a BEC.

The researchers started by preparing their gas of potassium atoms far from equilibrium (for instance by violently shaking the atomic cloud until it became completely disordered), and then allowed it to evolve on its own, driven only by the interactions between the particles. They then observed how the system settles down and becomes more orderly over time. At short distances, stronger interactions made the system relax faster, as expected. However, over larger distances, the relaxation speed showed a universal limit, where coherence grows at a universal rate not dependent upon the strength of interactions but just upon the ratio of Planck’s constant and the particle mass.

The speed limit D=3.4(3)ℏ/m, which the researchers have uncovered in their study, has fascinating consequences for how quickly coherence can form over large distances. For example, it would take centuries for coherence to spread in this way through a pool-sized potassium cloud. Even if the particles were as light as neutrons, it would take longer than the age of the universe for coherence to spread from London to New York.

“These results are exciting because they help us understand one of the most basic and broadly relevant questions about quantum matter,” says Dr Christoph Eigen, a researcher in the Hadzibabic Group (Quantum Gases and Collective Phenomena).

“The question of how a BEC forms was considered and debated already before the first BECs were made in 1995. The fact that we are only now able to access the universal behaviour is both surprising and exciting,” he adds.

The next challenge is to search for similar behaviour in other types of quantum matter and explore the practical implications of the speed limit, including the constraints on how large a fully ordered quantum system can be. This is both relevant for large synthetic quantum systems, and for large natural ones, such as neutron stars and dark matter candidates.

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