  Cold atomic gases offer the prospect of simulating the physics of the very
early universe in the laboratory. In the condensate phase, the gas is described
by a field theory with key features of high energy particle theory. This paper
describes a three level system which undergoes a first order phase transition
through the nucleation of bubbles. The theoretical investigation shows bubbles
nucleating in two dimensions at non-zero temperature. There is good agreement
between the bubble nucleation rates calculated from a Stochastic Projected
Gross-Pitaevskii equation and from a non-perturbative instanton method. When an
optical box trap is included in the simulations, the bubbles nucleate
preferentially near the walls of the trap.
