J Low Temp Phys (2007) 148: 423–427 DOI 10.1007/s10909-007-9399-5 Visibility of Vortex Core in Fermionic Superfluid with Population Imbalance M. Takahashi · T. Mizushima · K. Machida · M. Ichioka Published online: 30 May 2007 © Springer Science+Business Media, LLC 2007 Abstract In Fermionic superfluids with a vortex, at T = 0, the depletion of the atomic density appears in the core region, which is strongly associated with the discreteness of the core-bound state, called the Caroli-de Gennes-Matricon state. In imbalanced superfluid, however, it is found by the microscopic study based on the Bogoliubov-de Gennes approximation that this quantum depletion is progressively filled out in majority spin species as population imbalance increases. In contrast, the minority species keeps the depletion, which enables the direct observation of “super- fluidity”, because the quantized vortex is a hallmark of superfluidity. PACS 03.75.Ss · 03.75.Hh · 47.32.-y 1 Introduction The microscopic study on vortex core structure in “Fermionic” superfluid has a long history stretching back to the years immediately after the Bardeen-Cooper-Schrieffer theory [1] in 1957. The quantized vortex has a singular line at which the pairing is vanishing and the pairing recovers its bulk magnitude in the distance of the coherence length from the vortex line, that is, the pair potential forms a potential well in the vortex core region. The pioneering work for the quasiparticle eigenstates in a single vortex state has been done by Caroli et al. [2] in 1964, who identified the fact that the low-lying excitation spectrum appears inside the energy gap, whose wave function is tightly bounded in the vortex core region, called the Caroli-de Gennes-Matricon (CdGM) state. The further important concept as for quantized vortices is associated with the vis- ibility of the vortex, so-called the quantum depletion of the carrier density at the M. Takahashi ( ) · T. Mizushima · K. Machida · M. Ichioka Department of Physics, Okayama University, Okayama 700-8530, Japan e-mail: masahiro@mp.okayama-u.ac.jp