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The core structure of multiply quantized vortices is theoreticallyinvestigated in fermionic superfluid near Feshbach resonance. Under populationimbalance in two hyperfine spin states, the vortex core is filled in by the``paramagnetic moment''. Here, we find the spatial oscillation of themagnetization inside the core sensitively due to the topological structure ofthe pairing field, in the range from the weak coupling regime to the unitarylimit. This magnetization inside the giant core reveals the winding number ofthe vortex and directly results from the low-lying quasiparticle states boundinside the core. It is therefore proposed that the density profile experimentusing phase contrast imaging can provide the spectroscopy of novel core levelstructures in giant vortices. To help the understanding on these outcomes, wealso derive the analytic solution for the low-lying quasiparticle states insidethe core of a multiply quantized vortex.

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