1,2,3, Many – How Few Particles Turn into a ‘Heap’

How large does a group of particles have to be to render moot its exact number of particles?

In experiments using ultracold atoms, Heidelberg physicists succeeded in observing the transition to a many-body system well described by an infinite number of particles. In philosophy, this problem is known as the sorites paradox. The essential question is when a collection of elements forms a “heap”.

The experiments were conducted by researchers of Heidelberg University under the direction of Prof. Dr. Selim Jochim at the Max Planck Institute for Nuclear Physics. The results of the research were published in “Science”.

“Systems comprising many particles are generally extremely difficult to describe in a microscopically exact way. Hence researchers tend to work with effective theories that look not at the individual particles, such as gas molecules in the air, but at macroscopic values such as pressure or temperature,” explains Jochim. The Heidelberg researchers prepared the systems so small they could still be described microscopically. Starting with a single atom, the scientists increased the number of particles one by one.

The energy of the entire system was measured with each added particle. The experiments ultimately showed that for the system under study very few atoms were needed to apply the theory derived for an infinitely large system. “We can identify this as the direct transition from a few-body system into a many-body system. Simply put, in our system it takes only about four atoms to form a 'heap' in the sense of the sorites paradox,” continues the Heidelberg physicist.

Two years ago Jochim's team was able to reproducibly control the system used for the current experiments in all of its properties, including the exact number of particles, their state of motion and their interaction. “To date we are the only research team in the world able to prepare such systems,” Prof. Jochim points out. “For the first time, these results realise our vision to gain a much deeper insight into the nature of fundamental few-body systems by these experiments.

Original publication:
A. N. Wenz, G. Zürn, S. Murmann, I. Brouzos, T. Lompe, S. Jochim: From Few to Many: Observing the Formation of a Fermi Sea One Atom at a Time. Science, Vol. 342 no. 6157 pp. 457-460, 25 October 2013, doi: 10.1126/science.1240516
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