Spontaneous symmetry breaking in Bose–Einstein condensates

The structure of the many-particle wavefunction for a pair of ideal gas Bose–Einstein condensates a, b in the number eigenstate |NaNb〉 is analyzed. It is found that the most probable many-particle position or momentum measurement outcomes break the configurational phase symmetry of the state. Analytical expressions for the particle distribution and current density for a single experimental run are derived and found to display interference. Spontaneous symmetry breaking is thus predicted and explained here simply and directly as a highly probable measurement outcome for a state with a definite number of particles.