We study the orbital angular momentum (OAM)
Lz of two-dimensional chiral
(px+ipy)ν-wave superfluids (SFs) in the presence of an axisymmetric multiply quantized vortex (MQV) with vorticity
k on a disk at zero temperature, in the framework of Bogoliubov-de Gennes (BdG) theory. Focusing on spectral asymmetry (or spectral flow), we find that
Lz=(k+ν)N/2 for any integer
ν and
k in the Bose-Einstein Condensation (BEC) regime, where
N is the total number of fermions. While in the weak-pairing Bardeen-Cooper-Schrieffer (BCS) regime, only for chiral
p+ip-wave SF with
k=±1,
Lz=(k+ν)N/2 still holds. For chiral SFs with
ν≥2 or
∣k∣≥2 in the BCS regime, the OAM
Lz is remarkably reduced from its ``full" value in the BEC regime. However, the deviations differ in these two cases. For chiral SFs with
ν≥2,
Lz is sharply suppressed in this ideal setting with a specular wall, while the suppression caused by the
∣k∣≥2 vortex is moderate, which is core-size dependent. Furthermore, for
p+ip-wave SF with
k=−1, the total OAM
Lz is zero, but the distribution
Lz(r) is nontrivial compared with that of vortex-free
s-wave SF, in which the total OAM is zero as well. For chiral SFs with
ν≥2 and
∣k∣≥2, the effects of circulation due to vortex and chiral pairing can coexist, and hence depress the OAM simultaneously. These observations can be explained by spectral asymmetry and unpaired fermions in the ground state of the BdG Hamiltonian. We also investigate the spatial distribution of particle density, OAM, by solving the BdG equation.
Multiply quantized vortices in the BCS-to-BEC (Bose-Einstein condensation) evolution of
p-wave resonant Fermi gases are investigated theoretically. The vortex structure and the low-energy quasiparticle states are discussed, based on the self-consistent calculations of the Bogoliubov-de Gennes and gap equations. We reveal the direct relation between the macroscopic structure of vortices, such as particle densities, and the low-lying quasiparticle state. In addition, the net angular momentum for multiply quantized vortices with a vorticity $\ensuremath{\kappa}$ is found to be expressed by a simple equation, which reflects the chirality of the Cooper pairing. Hence, the observation of the particle density depletion and the measurement of the angular momentum will provide the information on the core-bound state and
p-wave superfluidity. Moreover, the details on the zero energy Majorana state are discussed in the vicinity of the BCS-to-BEC evolution. It is demonstrated numerically that the zero energy Majorana state appears in the weak coupling BCS limit only when the vortex winding number is odd. The $\ensuremath{\kappa}$ branches of the core-bound states for a vortex state with vorticity $\ensuremath{\kappa}$ exist; however, only one of them can be the zero energy. This zero energy state vanishes at the BCS-BEC topological phase transition because of interference between the core-bound and edge-bound states.
The structures of multiply quantized vortices (MQVs) of an equal-population atomic Fermi superfluid in a rotating spherical bubble trap approximated as a thin shell are analyzed by solving the Bogoliubov--de Gennes (BdG) equation throughout the Bardeen-Cooper-Schrieffer (BCS)--Bose-Einstein condensation (BEC) crossover. Consistent with the Poincar\'e-Hopf theorem, a pair of vortices emerge at the poles of the rotation axis in the presence of azimuthal symmetry and the compact geometry provides confinement for the MQVs. While the single-vorticity vortex structure is similar to that in a planar geometry, higher-vorticity vortices exhibit interesting phenomena at the vortex center, such as a density peak due to accumulation of a normal Fermi gas and reversed circulation of current due to in-gap states carrying angular momentum in the BCS regime but not the BEC regime because of the subtle relations between the order parameter and density. The energy spectrum shows the number of the in-gap state branches corresponds to the vorticity of a vortex, and an explanation based on a topological correspondence is provided.
The dynamics and interaction of quantized vortices in Bose-Einstein condensates (BECs) are investigated by using the two-dimensional Gross-Pitaevskii equation (GPE) with/without an angular momentum rotation term. If all vortices have the same winding number, they would rotate around the trap center but never collide. In contrast, if the winding numbers are different, their interaction highly depends on the initial distance between vortex centers. The analytical results are presented to describe the dynamics of the vortex centers when β=0. While if β≠0, there is no analytical result but some conclusive numerical findings are provided for the further understanding of vortex interaction in BECs. Finally, the dynamic laws describing the relation of vortex interaction in nonrotating and rotating BECs are presented.
We study the orbital angular momentum (OAM)
Lz in two-dimensional chiral $({p}_{x}+i{p}_{y}{)}^{\ensuremath{\nu}}$-wave superfluids (SFs) of
N fermions on a disk at zero temperature, in terms of spectral asymmetry and spectral flow. It is shown that ${L}_{z}=\ensuremath{\nu}N/2$ for any integer $\ensuremath{\nu}$, in the Bose-Einstein condensation regime. In contrast, in the BCS limit, while the OAM is
Lz=N/2 for the
p+ip-wave SF, for chiral SFs with $\ensuremath{\nu}\ensuremath{\ge}2$, the OAM is remarkably suppressed as ${L}_{z}=N\ifmmode\times\else\texttimes\fi{}O({\mathrm{\ensuremath{\Delta}}}_{0}/{ϵ}_{F})\ensuremath{\ll}N$, where ${\mathrm{\ensuremath{\Delta}}}_{0}$ is the gap amplitude and
ϵF is the Fermi energy. We demonstrate that the difference between the
p+ip-wave SF and the other chiral SFs in the BCS regimes originates from the nature of edge modes and related depairing effects.
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.