Anomalous coupling between topological defects and curvature

We investigate a counterintuitive geometric interaction between defects and curvature in thin layers of superfluids, superconductors and liquid crystals deposited on curved surfaces. Each defect feels a geometric potential whose functional form is determined only by the shape of the surface, but whose sign and strength depend on the transformation properties of the order parameter. For superfluids and superconductors, the strength of this interaction is proportional to the square of the charge and causes all defects to be repelled (attracted) by regions of positive (negative) Gaussian curvature. For liquid crystals in the one elastic constant approximation, charges between 0 and $4\pi$ are attracted by regions of positive curvature while all other charges are repelled.Comment: 5 pages, 4 figures, minor changes, accepted for publication in Phys. Rev. Let

Stability of the vortex lattice in a rotating superfluid

We analyze the stability of the vortex lattice in a rotating superfluid against thermal fluctuations associated with the long-wavelength Tkachenko modes of the lattice. Inclusion of only the two-dimensional modes leads formally to instability in infinite lattices; however, when the full three-dimensional spectrum of modes is taken into account, the thermally-induced lattice displacements are indeed finite.Comment: 16 page

Vortex lattices in rapidly rotating Bose-Einstein condensates: modes and correlation functions

After delineating the physical regimes which vortex lattices encounter in rotating Bose-Einstein condensates as the rotation rate, $\Omega$, increases, we derive the normal modes of the vortex lattice in two dimensions at zero temperature. Taking into account effects of the finite compressibility, we find an inertial mode of frequency $\ge 2\Omega$, and a primarily transverse Tkachenko mode, whose frequency goes from being linear in the wave vector in the slowly rotating regime, where $\Omega$ is small compared with the lowest compressional mode frequency, to quadratic in the wave vector in the opposite limit. We calculate the correlation functions of vortex displacements and phase, density and superfluid velocities, and find that the zero-point excitations of the soft quadratic Tkachenko modes lead in a large system to a loss of long range phase correlations, growing logarithmically with distance, and hence lead to a fragmented state at zero temperature. The vortex positional ordering is preserved at zero temperature, but the thermally excited Tkachenko modes cause the relative positional fluctuations to grow logarithmically with separation at finite temperature. The superfluid density, defined in terms of the transverse velocity autocorrelation function, vanishes at all temperatures. Finally we construct the long wavelength single particle Green's function in the rotating system and calculate the condensate depletion as a function of temperature.Comment: 11 pages Latex, no figure

Polygonal N-vortex arrays: A Stuart model

Published versio

Coherently Scattering Atoms from an Excited Bose-Einstein Condensate

We consider scattering atoms from a fully Bose-Einstein condensed gas. If we take these atoms to be identical to those in the Bose-Einstein condensate, this scattering process is to a large extent analogous to Andreev reflection from the interface between a superconducting and a normal metal. We determine the scattering wave function both in the absence and the presence of a vortex. Our results show a qualitative difference between these two cases that can be understood as due to an Aharonov-Bohm effect. It leads to the possibility to experimentally detect and study vortices in this way.Comment: 5 pages of ReVTeX and 2 postscript figure

Vortices and dynamics in trapped Bose-Einstein condensates

I review the basic physics of ultracold dilute trapped atomic gases, with emphasis on Bose-Einstein condensation and quantized vortices. The hydrodynamic form of the Gross-Pitaevskii equation (a nonlinear Schr{\"o}dinger equation) illuminates the role of the density and the quantum-mechanical phase. One unique feature of these experimental systems is the opportunity to study the dynamics of vortices in real time, in contrast to typical experiments on superfluid $^4$He. I discuss three specific examples (precession of single vortices, motion of vortex dipoles, and Tkachenko oscillations of a vortex array). Other unusual features include the study of quantum turbulence and the behavior for rapid rotation, when the vortices form dense regular arrays. Ultimately, the system is predicted to make a quantum phase transition to various highly correlated many-body states (analogous to bosonic quantum Hall states) that are not superfluid and do not have condensate wave functions. At present, this transition remains elusive. Conceivably, laser-induced synthetic vector potentials can serve to reach this intriguing phase transition.Comment: Accepted for publication in Journal of Low Temperature Physics, conference proceedings: Symposia on Superfluids under Rotation (Lammi, Finland, April 2010

Physics of Neutron Star Crusts

The physics of neutron star crusts is vast, involving many different research fields, from nuclear and condensed matter physics to general relativity. This review summarizes the progress, which has been achieved over the last few years, in modeling neutron star crusts, both at the microscopic and macroscopic levels. The confrontation of these theoretical models with observations is also briefly discussed.Comment: 182 pages, published version available at <http://www.livingreviews.org/lrr-2008-10

The Flux-Line Lattice in Superconductors

Magnetic flux can penetrate a type-II superconductor in form of Abrikosov vortices. These tend to arrange in a triangular flux-line lattice (FLL) which is more or less perturbed by material inhomogeneities that pin the flux lines, and in high-$T_c$ supercon- ductors (HTSC's) also by thermal fluctuations. Many properties of the FLL are well described by the phenomenological Ginzburg-Landau theory or by the electromagnetic London theory, which treats the vortex core as a singularity. In Nb alloys and HTSC's the FLL is very soft mainly because of the large magnetic penetration depth: The shear modulus of the FLL is thus small and the tilt modulus is dispersive and becomes very small for short distortion wavelength. This softness of the FLL is enhanced further by the pronounced anisotropy and layered structure of HTSC's, which strongly increases the penetration depth for currents along the c-axis of these uniaxial crystals and may even cause a decoupling of two-dimensional vortex lattices in the Cu-O layers. Thermal fluctuations and softening may melt the FLL and cause thermally activated depinning of the flux lines or of the 2D pancake vortices in the layers. Various phase transitions are predicted for the FLL in layered HTSC's. The linear and nonlinear magnetic response of HTSC's gives rise to interesting effects which strongly depend on the geometry of the experiment.Comment: Review paper for Rep.Prog.Phys., 124 narrow pages. The 30 figures do not exist as postscript file

Particles-vortex interactions and flow visualization in He4

Recent experiments have demonstrated a remarkable progress in implementing and use of the Particle Image Velocimetry (PIV) and particle tracking techniques for the study of turbulence in He4. However, an interpretation of the experimental data in the superfluid phase requires understanding how the motion of tracer particles is affected by the two components, the viscous normal fluid and the inviscid superfluid. Of a particular importance is the problem of particle interactions with quantized vortex lines which may not only strongly affect the particle motion, but, under certain conditions, may even trap particles on quantized vortex cores. The article reviews recent theoretical, numerical, and experimental results in this rapidly developing area of research, putting critically together recent results, and solving apparent inconsistencies. Also discussed is a closely related technique of detection of quantized vortices negative ion bubbles in He4.Comment: To appear in the J Low Temperature Physic