Condensed Matter Physics in New Places: From Nanotechnology to Atom Traps

The key finding of this project is that the thermodynamic limit for atom gases confined in a trap is singular. Let me explain what that means.

In systems consisting of a large number of particles, the behaviour is often perturbed by the edge of the container in which they are placed. For example, the flow of a fluid near the interior surface of its container often looks rather different from the flow in the bulk (far from the surface). These “edge effects” become less important as the system gets larger. To eliminate them completely, theorists often consider a hypothetical “thermodynamic limit”, in which:
- the container volume, V, is taken to infinity;
- the number of particles, N, is taken to infinity; but
- the ratio N/V (which is the density of particles) is held constant.
This eliminates edge effects by sending the edges infinitely far away.

Prior to my work, funded by this grant and undertaken in collaboration with researchers in Birmingham and Sao Paulo, it had always been assumed that a similar notion could be defined for a container of any shape. This is of particular relevance to experiments which confine cold atom gases in laser traps, because there the shape of the confining force field is very different from the kind of container you would put a gas in: roughly speaking, it’s more like a bowl than a box. What we showed is that:

(a) it is indeed possible to define a thermodynamic limit for any shape of the confining potential; but

(b) the thermodynamic-limit values for (for example) the energy per particle depend on the shape of the trap, even after the thermodynamic limit has been taken.

I don’t think anyone in the community expected result (b); indeed, we spent several years forcing it on their attention before it became widely accepted that what we were saying was true! Nowadays this result is commonly taken into account when designing cold-atom experiments in traps, and indeed several experimental groups have based their experimental designs on parts of the calculations we did in this project.