Spatial structure of a vortex in low density neutron matter

We study in a fully self-consistent approach the structure of a vortex in low density superfluid neutron matter. We determine that the matter density profile of a vortex shows a significant depletion in the region of the core, a feature never reported for a vortex state in a Fermi superfluid.     

Derivation of the transverse force on a moving vortex in a superfluid

We describe an exact derivation of the total nondissipative transverse force acting on a quantized vortex moving in a uniform background. The derivation is valid for neutral boson or fermion superfluids, provided the order parameter is a complex scalar quantity. The force is determined by the one-particle density matrix far away from the vortex core, and is found to be the Magnus force proportional to the superfluid density.     

Vortex-core structure in neutral fermion superfluids with population imbalance

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.     

Vortex state in a strongly coupled dilute atomic fermionic superfluid

We show that in a dilute fermionic superfluid, when the fermions interact with an infinite scattering length, a vortex state is characterized by a strong density depletion along the vortex core. This feature can make a direct visualization of vortices in fermionic superfluids possible.     

Berry phase effects on the dynamics of quasiparticles in a superfluid with a vortex

We study quasiparticle dynamics in a Bose-Einstein condensate with a vortex by following the center of mass motion of a Bogoliubov wave packet, and find important Berry-phase effects due to the background flow. We show that the Berry phase invalidates the usual canonical relation between the mechanical momentum and position variables, leading to important modifications of quasiparticle statistics and thermodynamic properties of the condensates. Applying these results to a vortex in an infinite uniform superfluid, we find that the total transverse force acting on the vortex is proportional to the superfluid density. We propose an experimental setup to directly observe Berry phase effects through measuring local thermal atoms' momentum distribution around a vortex.     

Aether as a superfluid state of particle-antiparticle pairs

A new model for the aether is suggested according to which it is a superfluid state of fermion and antifermion pairs, describable by a macroscopic wave function. The vacuum state of this superfluid pervades the entire universe and may account for the missing matter. The visible matter in the universe appears as excitations from the underlying superfluid vacuum.     

On the space-time curvature experienced by quasiparticle excitations in the Painlevé-Gullstrand effective geometry

We consider quasiparticle propagation in constant-speed-of-sound (iso-tachic) and almost incompressible (iso-pycnal) hydrodynamic flows, using the technical machinery of general relativity to investigate the “effective space-time geometry” that is probed by the quasiparticles. This effective geometry, described for the quasiparticles of condensed matter systems by the Painlevé-Gullstrand metric, generally exhibits curvature (in the sense of Riemann) and many features of quasiparticle propagation can be re-phrased in terms of null geodesics, Killing vectors, and Jacobi fields. As particular examples of hydrodynamic flow we consider shear flow, a constant-circulation vortex, flow past an impenetrable cylinder, and rigid rotation.     

Defect formation in inhomogeneous second-order phase transition: theory and experiment

The status quo in our understanding of defect formation during a rapid transition into the broken symmetry state in condensed matter and cosmology is discussed. An observation of vortex nucleation in neutron absorption experiments in superfluid ³He-B is interpreted in terms of defect formation during inhomogeneous cooling through T_c. Due to the temperature gradient in the locally heated region the superfluid-phase transition occurs as a propagating front. The theoretical considerations of vortex formation at the propagating front are based on works by Kibble–Volovik, Kopnin–Thuneberg, and Aranson–Kopnin–Vinokur (AKV).     

Topological aspects in a two-component Bose condensed system in neutron star

By making use of Duan--Ge's decomposition theory of gauge potential and the topological current theory proposed by Prof. Duan Yi-Shi, we study a two-component superfluid Bose condensed system, which is supposed to be realized in the interior of neutron stars in the form of the coexistence of a neutron superfluid and a protonic superconductor. We propose that this system possesses vortex lines. The topological charges of the vortex lines are characterized by the Hopf indices and the Brower degrees of φ-mapping.     

Macroscopic quantum phenomena in superfluids and superconductors

In this paper I will discuss the common macroscopic quantum phenomena in the three superfluid systems known in condensed matter, the superconducting state of a metal, the superfluid phase of liquid⁴He, and the superfluid phases of liquid³He. The discussed phenomena will be persistent currents and their decay, critical velocities and critical magnetic fields, quantization of magnetic flux and of circulation, the two-dimensional flux and vortex lattices, and eventually the Josephson effects.Invited paper at the International Conference on Macroscopic Quantum Phenomena, Smolenice Castle, Czechoslovakia, September 18–22, 1989.     

AdS/CFT Correspondence and Dark Soliton

In this paper we use the AdS/CFT correspondence to study dark soliton solutions in a holographic model of a relativistic superfluid. We calculate the length scales corresponding to the condensate and the charge density depletion, and find relation with the chemical potential. We compare our solutions with the quasiparticle excitations above the holographic superfluid and find that the scale of the excitations is comparable to the soliton coherence length scales.     

Superfluid nuclear matter calculations

We present a method to calculate nuclear matter properties in the superfluid phase. The method is based on the use of self-consistent off-shell nucleon propagators in the T-matrix equation. Such a complete treatment of the spectral function is required below and around T_c due to a pseudogap formation in the spectral function. In the superfluid phase we introduce the anomalous self-energy in the fermion propagators and in the T-matrix equation, consistently with the strong coupling BCS equations. The equations for the nucleon spectral function include both a contribution of condensed and scattering pairs. The method is illustrated by numerical calculations. Above T_c pseudogap formation is visible in the spectral function and below T_c a superfluid gap also appears.     

Majorana zero mode in the vortex of an artificial topological superconductor

Majorana fermion (MF), an exotic particle that is identical to its own antiparticle, was recently found in solid matter as a quasiparticle excitation, the Majorana zero mode (MZM), in the vortex of an artificial topological superconductor (TSC). This artificial TSC, first proposed by Fu and Kane in 2008, is a heterostructure made of a topological insulator Bi₂Te₃ and an s-wave superconductor NbSe₂. This paper will briefly review the experimental progresses based on the Bi₂Te₃/NbSe₂ heterostructure. All evidences are self-consistent and reveal that the MZM exists in the center of vortex. Those experimental results are also supported by theory. This finding is a milestone in the research of Majorana fermions in solid state physics and a starting point of MZM’s application in topological quantum computation.     

Superfluidity and superconductivity in relativistic fermion systems

The derivation of gap equations and Ginzburg-Landau free energies for relativistic fermion systems is reviewed. The cases of superfluid neutron matter, superconducting electrons and superconducting and colour superconducting quark matter are described in detail.     

Derivation of the Gross-Pitaevskii equation for condensed bosons from the Bogoliubov-de Gennes equations for superfluid fermions

We derive the time-independent Gross-Pitaevskii equation at zero temperature for condensed bosons, which form as bound-fermion pairs when the mutual fermionic attractive interaction is sufficiently strong, from the strong-coupling limit of the Bogoliubov-de Gennes equations that describe superfluid fermions in the presence of an external potential. Three-body corrections to the Gross-Pitaevskii equation are also obtained by our approach. Our results are relevant to the recent advances with ultracold fermionic atoms in a trap.     

Boson description of collective states: (II). Description of odd vibrational nuclei

By addition of the so-called ideal quasiparticle to the boson space one can represent the odd fermion states in that product space. In such a way one finds various representations of the fermion operators in terms of the boson operators and ideal quasiparticles. From these boson expansions of the fermion operators a finite one is selected by considering non-unitary transformations. Thus, the direct generalization, of the Dyson representation for even systems is given for the case of odd systems. The Hamiltonian can be divided into three parts: the boson term which describes the vibrational motion of the even core, the unperturbed motion of the quasiparticle, and the interaction between the quasiparticle and the bosons. This interaction consists of two terms, one of which agrees with the term used by Kisslinger and Sorensen ²), which is usually called the dynamical interaction, and the additional term is due to the antisymmetrization between the extra particle and the even core. The latter term can be identified as kinematical interaction which is responsible for the anomalous coupling states. For example, it is demonstrated that this term produces qualitatively the same splitting of the one-phonon multiplet as was obtained by Kuriyama et al. ³) for the j-shell. Furthermore, it is shown for the more complicated case of ¹¹⁷Sn that the effect of this additional interaction between phonons and quasiparticle is important when many shells to the states in the odd nucleus are taken into account.     

Delocalization in two-dimensional disordered Bose systems and depinning transition in the vortex state in superconductors

We investigate a two-dimensional (2D) Bose system with the long range interactions in the presence of disorder. Formation of the bound states at strong impurity sites gives rise to a depletion of the superfluid density. We predict the intermediate superfluid state where the condensate and localized bosons are present simultaneously. We find that interactions suppress localization and that with the increase of the boson density the system experiences a sharp delocalization crossover into a state where all bosons are delocalized. We map our results onto a 3D system of vortices in type II superconductors in the presence of columnar defects; the intermediate superfluid state maps to an intermediate vortex liquid where vortex liquid neighbors pinned vortices. We predict the depinning crossover within the vortex liquid and depinning induced vortex lattice-Bose glass melting.     

Quantum dynamics of a Bose superfluid vortex

We derive a fully quantum-mechanical equation of motion for a vortex in a 2-dimensional Bose superfluid in the temperature regime where the normal fluid density ρ(n)(T) is small. The coupling between the vortex "zero mode" and the quasiparticles has no term linear in the quasiparticle variables--the lowest-order coupling is quadratic. We find that as a function of the dimensionless frequency Ω=?Ω/k(B)T, the standard Hall-Vinen-Iordanskii equations are valid when Ω?1 (the "classical regime"), but elsewhere, the equations of motion become highly retarded, with significant experimental implications when Ω?1.