Phase transition dimensionality crossover from two to three dimensions in a trapped ultracold atomic Bose gas

The equilibrium properties of a weakly interacting atomic Bose gas across the Berezinskii-Kosterlitz-Thouless (BKT) and Bose-Einstein condensation (BEC) phase transitions are numerically investigated through dimensionality crossover from two to three dimensions. is realized by confining in an experimentally feasible hybridized trap which provides homogeneity along planar $xy$ directions box potential tandem with harmonic transverse $z$ direction. modified varying frequency tight loose trapping. Our findings, based on stochastic (projected) Gross-Pitaevskii equation, showcase continuous shift character transition BKT BEC, monotonic increase identified critical temperature as function dimensionality, strongest variation exhibited for small chemical values up approximately twice potential.