Simulating 2D-1D dimensional crossover with ultracold atoms

As a function of dimensionality, in quantum physics we have access to a broad range of phenomena. In this presentation, we describe the dimensional crossover along two integer dimensionalities, namely 2D to 1D, in strongly interacting ultracold atomic gases as a function of the transverse confining potential V_y. We showcase the analytical tools that can be used to describe the large V_y case where the system is well described by weakly-coupled chains, such as bosonization. In this regime, we use a mean-field approach to decouple the chains and study the temperature at which we expect the crossover to occur and it’s scaling as a function of V_y. We extend the analysis to a broader range of V_y by meaning of QMC simulations and study the superfluid fraction and the evolution of the one-body density matrix g₁(x) by comparing with experiment. These results allow us to define in the V_y - k_bT plane a phase diagram which ranges from BKT physics to 1D Luttinger liquid going through a distinct intermediate phase.