Energy cost associated with vortex crossing in superconductors

Starting from the Ginzburg-Landau free energy of a type II superconductor in a magnetic field we estimate the energy associated with two vortices crossing. The calculations are performed by assuming that we are in a part of the phase diagram where the lowest Landau level approximation is valid. We consider only two vortices but with two markedly different sets of boundary conditions: on a sphere and on a plane with quasi-periodic boundary conditions. We find that the answers are very similar suggesting that the energy is localised to the crossing point. The crossing energy is found to be field and temperature dependent -- with a value at the experimentally measured melting line of $U_\times \simeq 7.5 k T_m \simeq 1.16/c_L^2$, where $c_L$ is the Lindemann melting criterion parameter. The crossing energy is then used with an extension of the Marchetti, Nelson and Cates hydrodynamic theory to suggest an explanation of the recent transport experiments of Safar {{\em et al.}\ }.Comment: 15 pages, RevTex v3.0, followed by 5 postscript figure

Anomalous hydrodynamics and "normal" fluids in rapidly rotating BECs

In rapidly rotating bose systems we show that there is a region of anomalous hydrodynamics whilst the system is still condensed, which coincides with the mean field quantum Hall regime. An immediate consequence is the absence of a normal fluid in any conventional sense. However, even the superfluid hydrodynamics is not described by conventional Bernoulli and continuity equations. We show there are kinematic constraints which connect spatial variations of density and phase, that the positions of vortices are not the simplest description of the dynamics of such a fluid (despite their utility in describing the instantaneous state of the condensate) and that the most compact description allows solution of some illuminating examples of motion. We demonstrate, inter alia, a very simple relation between vortices and surface waves. We show the surface waves can form a "normal fluid" which absorbs energy and angular momentum from vortex motion in the trap. The time scale of this process is sensitive to the initial configuration of the vortices, which can lead to long-lived vortex patches - perhaps related to those observed at JILA.Comment: 4 pages; 1 sentence and references modifie

Exact vortex nucleation and cooperative vortex tunneling in dilute BECs

With the imminent advent of mesoscopic rotating BECs in the lowest Landau level (LLL) regime, we explore LLL vortex nucleation. An exact many-body analysis is presented in a weakly elliptical trap for up to 400 particles. Striking non-mean field features are exposed at filling factors >>1 . Eg near the critical rotation frequency pairs of energy levels approach each other with exponential accuracy. A physical interpretation is provided by requantising a mean field theory, where 1/N plays the role of Planck's constant, revealing two vortices cooperatively tunneling between classically degenerate energy minima. The tunnel splitting variation is described in terms of frequency, particle number and ellipticity.Comment: 4 pages,4 figure

Implementation and modeling of a femtosecond laser-activated streak camera

8 June 2017) A laser-activated streak camera was built to measure the duration of femtosecond electron pulses. The streak velocity of the device is 1.89 mrad/ps, which corresponds to a sensitivity of 34.9 fs/pixels. The streak camera also measures changes in the relative time of arrival between the laser and electron pulses with a resolution of 70 fs RMS. A full circuit analysis of the structure is presented to describe the streaking field and the general behavior of the device. We have developed a general mathematical model to analyze the streaked images. The model provides an accurate method to extract the pulse duration based on the changes of the electron beam profile when the streaking field is applied

Condensation of `composite bosons' in a rotating BEC

We provide evidence for several novel phases in the dilute limit of rotating BECs. By exact calculation of wavefunctions and energies for small numbers of particles, we show that the states near integer angular momentum per particle are best considered condensates of composite entities, involving vortices and atoms. We are led to this result by explicit comparison with a description purely in terms of vortices. Several parallels with the fractional quantum Hall effect emerge, including the presence of the Pfaffian state.Comment: 4 pages, Latex, 3 figure

Exact Eignstates for Trapped Weakly Interacting Bosons in Two Dimensions

A system of N two-dimensional weakly interacting bosons in a harmonic trap is considered. When the two-particle potential is a delta function Smith and Wilkin have analytically proved that the elementary symmetric polynomials of particle coordinates measured from the center of mass are exact eigenstates. In this study, we point out that their proof works equally well for an arbitrary two-particle potential which possesses the translational and rotational symmetries. We find that the interaction energy associated with the eigenstate with angular momentum L is equal to aN(N-1)/2+(b-a)NL/2, where a and b are the interaction energies of two bosons in the lowest-energy one-particle state with zero and one unit of angular momentum, respectively. Additionally, we study briefly the case of attractive quartic interactions. We prove rigorously that the lowest-energy state is the one in which all angular momentum is carried by the center of mass motion.Comment: 4 pages, minor changes made, to appear in PRA Brie

Weakly Interacting Bose-Einstein Condensates Under Rotation: Mean-field versus Exact Solutions

We consider a weakly-interacting, harmonically-trapped Bose-Einstein condensed gas under rotation and investigate the connection between the energies obtained from mean-field calculations and from exact diagonalizations in a subspace of degenerate states. From the latter we derive an approximation scheme valid in the thermodynamic limit of many particles. Mean-field results are shown to emerge as the correct leading-order approximation to exact calculations in the same subspace.Comment: 4 pages, RevTex, submitted to PR

Quantum Phases of Vortices in Rotating Bose-Einstein Condensates

We investigate the groundstates of weakly interacting bosons in a rotating trap as a function of the number of bosons, $N$, and the average number of vortices, $N_V$. We identify the filling fraction $\nu\equiv N/N_V$ as the parameter controlling the nature of these states. We present results indicating that, as a function of $\nu$, there is a zero temperature {\it phase transition} between a triangular vortex lattice phase, and strongly-correlated vortex liquid phases. The vortex liquid phases appear to be the Read-Rezayi parafermion states

Plastic energies in layered superconductors

We estimate the energy cost associated with two pancake vortices colliding in a layered superconductor. It is argued that this energy sets the plastics energy scale and is the analogue of the crossing energy for vortices in the continuum case. The starting point of the calculation is the Lawrence-Doniach version of the Ginzburg-Landau free energy for type-II superconductors. The magnetic fields considered are along the c-direction and assumed to be sufficiently high that the lowest Landau level approximation is valid. For Bi-2212, where it is know that layering is very important, the results are radically different from what would have been obtained using a three-dimensional anisotropic continuum model. We then use the plastic energy for Bi-2212 to successfully explain recent results from Hellerqvist {\em et al.}\ on its longitudinal resistance.Comment: 5 Pages Revtex, 4 uuencoded postscript figure