Exact analytical results for density profile in Fourier space and elastic scattering function of a rotating harmonically confined ultra-cold Fermi gas

In this paper, the system dealt with consisting of an ultra-cold neutral spin-polarized Fermi gas undergoing rotation (or in the so-called synthetic magnetic field) trapped by an anisotropic harmonic potential in a two and three-dimensional space at zero temperature. Using the so-called Bloch propagator as a tool, we derive exact closed-form expressions for particle density in Fourier space which are valid for an arbitrary particle number confined by a two and three-dimensional rotating anisotropic harmonic trap. Numerical illustrations and discussions are presented. The results can be easily generalized at finite temperatures. The crossover from two-dimensional to the one-dimensional regime is shown to be reflected in the shape of the density distribution in Fourier space at very fast rotating velocity (or at strong synthetic magnetic field). In addition, an exact analytical expression of the elastic scattering factor is found, a quantity of interest used to probe the spatial distribution of the quantum gases.