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arXiv:0911.2964 · Journal of the Physical Society of Japan

Stability of the Singular Vortex and Associated Majorana Zero Modes in Trapped p-Wave Resonant Superfluids of Neutral Cold Atoms

Yasumasa Tsutsumi, Kazushige Machida

Published Mar 10, 2010• 5 citations
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Abstract

The stability conditions for the singular vortex which accompanies Majorana zero modes at the core are investigated for p-wave resonant superfluids of atomic Fermi gases. Within the Ginzburg-Landau framework we determine the stable conditions in the parameter space for the external rotation frequency and the harmonic trap frequency. There exists the narrow stable region in this parameter space for quasi-two-dimensional condensates. We also describe the detailed characterizations of the spatial structure of the order parameter in the chiral p-wave superfluids under rotation.

DOI
10.1143/jpsj.79.034301

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We study the superfluid phases of quasi-two-dimensional atomic Fermi gases interacting via a ppp-wave Feshbach resonance. We calculate the absorption spectra of these phases under a hyperfine transition for both nonrotating and rotating superfluids. We show that one can identify the different phases of the ppp-wave superfluid from the absorption spectrum. The absorption spectrum shows clear signatures of the existence of Majorana zero modes at the cores of vortices of the weakly pairing px+ipy{p}_{x}+i{p}_{y}px​+ipy​ phase.
Fundamental properties of superfluids with d-wave pairing symmetry are investigated theoretically. We consider neutral atomic Fermi gases in a harmonic trap, the Cooper pairing being produced by a Feshbach resonance via a d-wave interaction channel. A Ginzburg-Landau (GL) functional is constructed which is symmetry constrained for five component order parameters (OPs). We find stable OP textures and vortices for all the three phases which are known to be the energy minimum of the GL functional; the ferromagnetic, polar and cyclic phases both at rest and under rotation. In particular, we touch upon the stability conditions for a non-Abelian fractional 1/3-vortex in the cyclic phase under rotation. It is proposed how to create the intriguing 1/3-vortex experimentally in atomic gases via optical means.
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We study Majorana modes in the vortex core of a two-dimensional p+ipp+ipp+ip Fermi superfluid interacting with a Bose-Einstein condensate. Under a repulsive sss-wave contact interaction between fermions and bosons, fermions are depleted from the vortex core when the bosonic density becomes sufficiently high. This gives rise to a dynamically driven local interface that emerges between fermions and bosons, along which chiral Majorana edge states should appear. We examine in detail the variation of vortex-core structures as well as the formation of chiral Majorana edge states with increasing bosonic density, where the circulation of the vortex plays an important role. Whereas both the Majorana modes and the vortex-core structures can be controlled and manipulated by tuning the bosonic density and the Bose-Fermi interaction strength, our study presents an illuminating example of how topological defects can be dynamically controlled in the context of cold-atomic gases.
In this paper, we study the structure of vortex lattices in a trapped superfluid Fermi gas in the unitary region near the superfluid transition temperature. A phenomenological approach based on the Ginzburg-Landau theory is used. Two types of stable triangular vortex lattices are found numerically at the same rotation frequency. In type (A), the trap center is occupied by a vortex; in type (B), there are three vortices closest to the trap center which is unoccupied. The lattice structures at different rotation frequencies and temperatures are analyzed. The vortex density increases linearly with the rotation frequency, very close to the analytical estimation. The superfluid and type-(B) vortex lattice do not disappear together. At high rotation frequencies, the vortex lattice disappears, but there exists a localized superfluid state near the trap center. The superfluid vanishes at a critical rotation frequency consistent with the theory for the upper critical magnetic field of type-II superconductors.