Magnetization profile and core level spectroscopy in a multiply quantized vortex of imbalanced Fermi superfluids

The core structure of multiply quantized vortices is theoretically investigated in fermionic superfluid near Feshbach resonance. Under population imbalance in two hyperfine spin states, the vortex core is filled in by the ``paramagnetic moment. Here, we find the spatial oscillation of the magnetization inside the core sensitively due to the topological structure of the pairing field, in the range from the weak coupling regime to the unitary limit. This magnetization inside the giant core reveals the winding number of the vortex and directly results from the low-lying quasiparticle states bound inside the core. It is therefore proposed that the density profile experiment using phase contrast imaging can provide the spectroscopy of novel core level structures in giant vortices. To help the understanding on these outcomes, we also derive the analytic solution for the low-lying quasiparticle states inside the core of a multiply quantized vortex.