Effect of harmonic confinement on correlation studies of a spin-polarized s-wave superconductor

We have investigated a spin imbalanced s-wave superconductor on a two-dimensional lattice in presence of a harmonic confinement. The nature of the order parameter and magnetization change as the trap effects are switched off. Other physical quantities show that trap effects suppress the distinction between spin balanced and imbalanced cases. We study different correlation functions for a spin imbalanced and harmonically trapped Fermi gas in two dimensions described by an attractive Hubbard model. Eigensolutions obtained via numerically solving Bogoliubov de Gennes equations are used to compute the local pairing amplitudes which show significantly different behaviour for the trapped case where the profile is radially modulated in contrast with a spatial modulation extending throughout the lattice geometry when trap effects are switched off. Further, different experimentally accessible quantities, such as pair-pair, density-density correlations and local density fluctuations show characteristic fluctuations for the spin polarized phase, which however wash away as the trapping effects are turned on. A contrasting scenario is presented corresponding to the case when the spin polarization effects are turned off.