Number Of Vortex Lines Research Articles

Tubular laser solitons.

We analyze, to the best of our knowledge, a new type of topological optical solitons in lasers with fast saturable absorption, which is intermediate between 2D and 3D ones. Being generated by 2D laser solitons, such 3D dissipative solitons in a laser cavity of length L have a number of vortex lines, which are straight for under-critical values L and spiral for larger L. For supercritical L, a vortex with multiple topological charges m>1 in generating 2D solitons transforms into m separate vortex lines. Taking into account weak non-paraxiality reveals polarization singularities in the form of lines, on which the elliptical polarization turns into linear in the cross section of the structures.

Rotating spin-1/2 Bose–Einstein condensates in a gradient magnetic field with spin–orbit coupling

We study the ground-state phases of two-dimensional rotating spin–orbit coupled spin-1/2 Bose–Einstein condensates (BECs) in a gradient magnetic field. The competition between gradient magnetic field, spin–orbit coupling and rotation leads to a variety of ground-state phase structures. In the weakly rotation regime, as the increase of gradient magnetic field strength, the BECs experiences a phase transition from the unstable phase to the single vortex-line phase. The unstable phase presents the vortex lines structures along the off-diagonal direction. With magnetic field gradient strength increasing, the number of vortex lines changes accordingly. As the magnetic field gradient strength increases further, the single vortex-line phase with a single vortex line along the diagonal direction is formed. The phase diagram shows that the boundary between the two phases is linear with the relative repulsion λ ≥ 1 and is nonlinear with λ < 1. In the relatively strong rotation regime, in addition to the unstable phase and the single vortex-line phase, the vortex-ring phase is formed for the strong magnetic field gradient and rapid rotation. The vortex-ring phase shows the giant and hidden vortex structures at the center of ring. The strong magnetic field gradient makes the number of the vortices around the ring unchanged.

Oscillatory superfluid Ekman pumping in helium II and neutron stars

The linear response of a superfluid, rotating uniformly in a cylindrical container and threaded with a large number of vortex lines, to an impulsive increase in the angular velocity of the container is investigated. At zero temperature and with perfect pinning of vortices to the top and bottom of the container, we demonstrate that the system oscillates persistently with a frequency proportional to the vortex line tension parameter to the quarter power. This low-frequency mode is generated by a secondary flow analogous to classical Ekman pumping that is periodically reversed by the vortex tension in the boundary layers. We compare analytic solutions to the two-fluid equations by Chandler &amp; Baym (J. Low Temp. Phys., vol. 62, 1986, pp. 119–142) with the spin-up experiments by Tsakadze &amp; Tsakadze (J. Low Temp. Phys., vol. 39, 1980, pp. 649–688) in helium II and find that the frequency agrees within a factor of four, although the experiment is not perfectly suited to the application of linear theory. We argue that this oscillatory Ekman pumping mode, and not Tkachenko modes, provides a natural explanation for the observed oscillation. In neutron stars, the oscillation period depends on the pinning interaction between neutron vortices and flux tubes in the outer core. Using a simplified pinning model, we demonstrate that strong pinning can accommodate modes with periods of days to years, which are only weakly damped by mutual friction over longer time scales.

Vortex lines distribution in inhomogeneous lattices

We study the distribution of vortex lines in a three-dimensional lattice with inhomogeneous couplings. We investigate the spatial distribution of the number of vortex lines, showing how the vortex lines are expelled from the region with higher couplings. Results for the correlation functions are presented, together with a discussion of the implications of the obtained results for the vortex distribution in ultracold trapped gases and in neutron stars.

On statistical mechanics of vortex lines

An ensemble of a large number of vortex lines in cylindrical bounded domain is being considered. A system of equations determining the statistical characteristics of vortex line motion is derived from the assumption that this motion is ergodic and vortex lines are sufficiently smooth. The smoothness of vortex lines is characterized by vortex diffusivity. Both cases of finite and infinite vortex diffusivity are discussed. The continuum limit equations are obtained.

NMR Spectroscopy of the Double-Quantum Vortex in Superfluid 3He-A

The double-quantum vortex line with continuous (singularity-free) structure is the most common linear defect in rotating 3 He-A. Its well-known experimental signature is a frequency-shifted satellite peak in the NMR spectrum. It arises from the absorption of spin wave excitations, which are localized bound states in the dipole-unlocked soft vortex core. In first approximation, the intensity of the satellite peak is proportional to the number of vortex lines. With increased measuring resolution we have found that the absorption contribution of individual vortex lines is not identical, but displays small variations, which depend on the non-uniform global orbital 1 texture. We attribute the effect to small texture-dependent changes in the 1 distribution in the soft core, which modify the attractive potential of the localized spin waves. This property can be used for studying the global order-parameter texture in the rotating container.

NMR line shape of rotating 3He-B at large counterflow velocity

We have investigated the NMR line shapes of superfluid 3He-B in a rotating cylinder. In the vortex-free state at sufficiently large angular velocity of rotation, Ω≳1 rad/s, the main feature of the absorption spectrum is a large frequency-shifted peak above the Larmor frequency. The shape of this counterflow peak is both measured and calculated as a function of external magnetic field strength, angular velocity, temperature, and number of vortex lines. The NMR spectrum is derived from the calculated order-parameter texture. Reasonable agreement with the measured line shape is obtained by including line-broadening effects due to the external field inhomogeneity and Leggett–Takagi relaxation.

Annihilation of quantized vortex lines in rotating3He-A

The maximum number of vortex lines at a given angular velocity Ω is obtained during deceleration when vortices annihilate at the wall of the container. The width of the vortex-free region in the decelerated state has been measured by cw NMR for vortex lines with singular and continuous core structures. It corresponds to the limit of stability of peripheral vortices for single and double quantization respectively.