Two-Point Momentum and Spatial Correlations of Few Ultracold Quasi-One-Dimensional Trapped Fermions: Diffraction Patterns

Spatial and momentum correlations are important in the analysis of the quantum states and different phases of trapped ultracold atom systems as a function of the strength of interatomic interactions. Identification and understanding of spin-resolved patterns exhibited in two-point correlations are key for uncovering the symmetry and structure of the many-body wavefunctions of the trapped system. Using the full configuration interaction method for diagonalization of the many-body Hamiltonian with 2 to 4 fermionic atoms trapped in single or multiple wells, we analyze two-point spatial and momentum space correlations and noise distributions, for a broad range of interparticle contact repulsion strengths and interwell separations, unveiling characteristics allowing insight into the transition from the intermediate quasi BEC regime to the strong-repulsion Tonks-Giradeau (TG) phase. The ab-initio numerical predictions agree well with those from our analytical model. The two-point momentum correlation is found to exhibit damped oscillatory diffraction behavior, which fully develops for atoms trapped in a single well with strong interatomic repulsion in the TG regime, or for atoms in well-separated multi-well traps [arXiv:1710.07853] .