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Collective behaviour emerges particle by particle

many-body system
Six pairs of atoms in the focus of a laser beam. (Courtesy: Jonas Ahlstedt/Lund University Bioimaging Centre (LBIC))

An ensemble of just six atoms displays all the signatures of a phase transition expected for a many-particle system. This is the finding of a team led by researchers at the University of Heidelberg, Germany, who used a quantum simulator to investigate how collective behaviour emerges in a microscopic structure. The new work advances our understanding of many-body physics, which describes phenomena that cannot be understood simply by studying the behaviour of individual particles.

Theories of many-body physics ignore the microscopic details of particle behaviour and focus instead on macroscopically observable quantities such as pressure, temperature and density. A system such as a glass of water, for example, might be described in a way that neglects the position and velocity of individual water molecules – even though the system’s macroscopic properties are the result of interaction between such molecules – once the number of water molecules reaches a certain critical size.

But what is that critical size? In other words, how big does an ensemble of particles need to be before their exact number becomes irrelevant and the entire system can be described using many-body theories? The transition from “discrete” to “continuous” behaviour has important implications in atomic, nuclear and solid-state physics, but determining exactly when it occurs has proved difficult. What is more, while the microscopic behaviour of each individual particle might be easy to describe exactly, the macroscopic behaviour of the particles as they interact is not.

Quasi-two-dimensional quantum simulator

A team led by Selim Jochim of the University of Heidelberg’s Institute of Physics tackled this problem by trapping up to 12 ultracold lithium-6 (6Li) atoms, assembled in two internal hyperfine states, at the focus of a laser beam. The trap’s geometry is such that the atoms can move in just two spatial directions, meaning that the system is effectively two-dimensional. The researchers then applied a special cooling technique that brought the system very close to its motional ground state, at a temperature just above absolute zero. This set-up also allowed the researchers to continuously tune the strength of the interactions between the atoms via an applied magnetic field, using so-called Feshbach resonances.

In their experiments, Jochim and colleagues configured the applied magnetic field so that the atoms attracted one another. If the attraction was strong enough, the atom formed pairs that could subsequently undergo a phase transition to a superfluid (a state in which the particles flow without friction). The researchers then observed how the atoms formed pairs as a function of their interaction strength and their number by measuring the binding energy of the atom pairs. To their surprise, they found that the atoms behaved like a many-body system even with only six atoms present.

Precursors of a quantum phase transition

Study lead authors Luca Bayha and Marvin Holten note that the type of pairing they studied is the precursor of a quantum phase transition to a superfluid phase with an associated “Higgs mode”. This mode has previously been observed in cold-atom, superconducting and ferromagnetic systems, but Bayha and Holten say that their work casts fresh light on how it arises. “Our atomic simulator provides a way to study the emergence of collective phenomena, particle by particle,” they say.

Members of the team, which also includes collaborators at the universities of Lund, Sweden, and Aarhus, Denmark, say they are now planning to study superfluidity in such mesoscopic systems in much more detail. “We will also use a novel imaging method to resolve each atom in our sample separately,” Bayha and Holten tell Physics World. “This will allow us to reveal the atom pairs that form in the superfluid state directly.”

The present work is detailed in Nature.

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