Fock State Sampling Method — Characteristic Temperature of Maximal Fluctuations for Interacting Bosons in Box Potentials

Abstract

We study the statistical properties of a gas of interacting bosons trapped in a box potential in two and three dimensions. Our primary focus is the characteristic temperature T_p, i.e., the temperature at which the fluctuations of the number of condensed atoms (or, in 2D, the number of motionless atoms) are maximal.  Using  the Fock state sampling method,  we  show  that T_p increases due to interaction. In 3D, this temperature converges to the critical temperature in the thermodynamic limit. In 2D, we show the general applicability of the method by obtaining a generalized dependence of the characteristic temperature on the interaction strength. Finally, we discuss the experimental conditions necessary for the verification of our theoretical predictions.