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arXiv:cond-mat/0607147 · Physical Review Letters

Vortex-Core Structure in Neutral Fermion Superfluids with Population Imbalance

Masahiro O. Takahashi, Takeshi Mizushima, Masanori Ichioka, K. Machida

Published Nov 1, 2006• 27 citations
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Abstract

Quantized vortex-core structure is theoretically investigated in fermion superfluids with population imbalance for two atom species of neutral atom clouds near a Feshbach resonance. In contrast with the vortex core in balance case where the quantum depletion makes a vortex visible through the density profile measurement, the vortex core is filled in and becomes less visible because the quantized discrete bound states are occupied exclusively by the majority species. Yet it is shown that the core can be visible through the minority density profile experiment using phase contrast imaging, revealing an interesting opportunity to examine low-lying fermionic core bound states unexplored so far.

DOI
10.1103/physrevlett.97.180407

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Quantized vortex-core structure is theoretically investigated in fermion superfluids with population imbalance for two atom species of neutral atom clouds near a Feshbach resonance. In contrast with the vortex core in balance case where the quantum depletion makes a vortex visible through the density profile measurement, the vortex core is filled in and becomes less visible because the quantized discrete bound states are occupied exclusively by the majority species. Yet it is shown that the core can be visible through the minority density profile experiment using phase contrast imaging, revealing an interesting opportunity to examine low-lying fermionic core bound states unexplored so far.
The core structure of multiply quantized vortices is theoretically investigated in a 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 understand these outcomes, we also derive an analytic solution for the low-lying quasiparticle states inside the core of a multiply quantized vortex.
We analyze the vortex core states of two-species (mass imbalanced) superfluid fermion mixtures as a function of two-body binding energy in two dimensions. In particular, we solve the Bogoliubov--de Gennes equations for a population balanced mixture of 6Li^{6}\mathrm{Li}6Li and 40K^{40}\mathrm{K}40K atoms at zero temperature. We find that the vortex core is mostly occupied by the light-mass (6Li)(^{6}\mathrm{Li})(6Li) fermions and that the core density of the heavy-mass (40K)(^{40}\mathrm{K})(40K) fermions is highly depleted. This is in contrast with the one-species (mass balanced) mixtures with balanced populations where an equal amount of density depletion is found at the vortex core for both pseudospin components.
The structure of multiply quantized or giant vortex states in atomic Fermi gases across a Feshbach resonance is studied within the context of self-consistent Bogoliubov--de Gennes theory. The particle density profile of vortices with $\ensuremath{\kappa}>1$ flux quanta is calculated. Owing to $\ensuremath{\kappa}$ discrete branches of vortex-core bound states, inside the core the density oscillates as a function of the distance from the vortex line and displays a nonmonotoic dependence on the interaction strengths, in marked contrast to the singly quantized case, in which the density depletes monotonically. This feature can make a direct visualization of the giant vortices in atomic Fermi gases.
In order to clarify the structure of a singly quantized vortex in a superfluid fermion gas near the Feshbach resonance, we numerically solve the generalized Bogoliubov-de Gennes equation in the boson-fermion model. The superfluid gap, which contains contributions from both condensed fermion pairs and condensed bosons, is self-consistently determined, and the quasiparticle excitation levels bound in the vortex core are explicitly shown. We find that the boson condensate contributes to enhance the matter density depletion and the discreteness of localized quasiparticle spectrum inside the core. It is predicted that the matter density depletion and the discrete core levels are detectable in the vicinity of the BCS-Bose-Einstein condensation crossover point.
In order to understand what kind of information can be extracted from the vortex-core structure in superfluid fermion-atom gases we make a systematic study for the core structure of a singly quantized vortex in the range of broad Feshbach resonance, solving numerically the generalized Bogoliubov--de Gennes equation derived from the fermion-boson model. Numerical calculations reveal that the vortex core can be well characterized by three length scales from the spatial variation of the fermionic and bosonic gap functions. We also predict that the profile of matter depletion and the quasiparticle spectrum show distinctive differences between the BCS and Bose-Einstein Condensate regimes.
We study a single quantized vortex in the fermionic component of a mixture of Fermi superfluid and Bose-Einstein condensate. As the density ratio between the boson and the fermion components is tuned, we identify a transition in the vortex-core structure, across which fermions in the vortex core become completely depleted even in the weak-coupling Bardeen-Cooper-Schrieffer regime. This is accompanied by changes in key properties of the vortex state, as well as by the localization of the Bose-Einstein condensate in the vortex core. The transition in the vortex-core structure can be experimentally probed in Bose-Fermi superfluid mixtures by detecting the size and visibility of the vortices.