Fluxon analogues and dark solitons in linearly coupled Bose-Einstein condensates

Two effectively one-dimensional parallel coupled Bose-Einstein condensates in the presence of external potentials are studied. The system is modelled by linearly coupled Gross-Pitaevskii equations. In particular, grey-soliton-like solutions representing analogues of superconducting Josephson fluxons as well as coupled dark solitons are discussed. Theoretical approximations based on variational formulations are derived. It is found that the presence of a magnetic trap can destabilize the fluxon analogues. However, stabilization is possible by controlling the effective linear coupling between the condensates.Comment: 14 pages, 7 figures, The paper is to appear in Journal of Physics

Beating dark-dark solitons in Bose-Einstein condensates

Motivated by recent experimental results, we study beating dark-dark solitons as a prototypical coherent structure that emerges in two-component Bose-Einstein condensates. We showcase their connection to dark- bright solitons via SO(2) rotation, and infer from it both their intrinsic beating frequency and their frequency of oscillation inside a parabolic trap. We identify them as exact periodic orbits in the Manakov limit of equal inter- and intra-species nonlinearity strengths with and without the trap and showcase the persistence of such states upon weak deviations from this limit. We also consider large deviations from the Manakov limit illustrating that this breathing state may be broken apart into dark-antidark soliton states. Finally, we consider the dynamics and interactions of two beating dark-dark solitons in the absence and in the presence of the trap, inferring their typically repulsive interaction.Comment: 13 pages, 14 figure

Oscillons and oscillating kinks in the Abelian-Higgs model

We study the classical dynamics of the Abelian Higgs model employing an asymptotic multiscale expansion method, which uses the ratio of the Higgs to the gauge field amplitudes as a small parameter. We derive an effective nonlinear Schr\"{o}dinger equation for the gauge field, and a linear equation for the scalar field containing the gauge field as a nonlinear source. This equation is used to predict the existence of oscillons and oscillating kinks for certain regimes of the ratio of the Higgs to the gauge field masses. Results of numerical simulations are found to be in very good agreement with the analytical findings, and show that the oscillons are robust, while kinks are unstable. It is also demonstrated that oscillons emerge spontaneously as a result of the onset of the modulational instability of plane wave solutions of the model. Connections of the obtained solutions with the phenomenology of superconductors is discussed.Comment: arXiv admin note: substantial text overlap with arXiv:1306.386

Dark solitons and vortices in PT-symmetric nonlinear media: from spontaneous symmetry breaking to nonlinear PT phase transitions

We consider nonlinear analogues of Parity-Time (PT) symmetric linear systems exhibiting defocusing nonlinearities. We study the ground state and excited states (dark solitons and vortices) of the system and report the following remarkable features. For relatively weak values of the parameter $\varepsilon$ controlling the strength of the PT-symmetric potential, excited states undergo (analytically tractable) spontaneous symmetry breaking; as $\varepsilon$ is further increased, the ground state and first excited state, as well as branches of higher multi-soliton (multi-vortex) states, collide in pairs and disappear in blue-sky bifurcations, in a way which is strongly reminiscent of the linear PT-phase transition ---thus termed the nonlinear PT-phase transition. Past this critical point, initialization of, e.g., the former ground state leads to spontaneously emerging solitons and vortices.Comment: 8 pages, 8 figure

Single and Multiple Vortex Rings in Three-Dimensional Bose-Einstein Condensates: Existence, Stability and Dynamics

In the present work, we explore the existence, stability and dynamics of single and multiple vortex ring states that can arise in Bose-Einstein condensates. Earlier works have illustrated the bifurcation of such states, in the vicinity of the linear limit, for isotropic or anisotropic three-dimensional harmonic traps. Here, we extend these states to the regime of large chemical potentials, the so-called Thomas-Fermi limit, and explore their properties such as equilibrium radii and inter-ring distance, for multi-ring states, as well as their vibrational spectra and possible instabilities. In this limit, both the existence and stability characteristics can be partially traced to a particle picture that considers the rings as individual particles oscillating within the trap and interacting pairwise with one another. Finally, we examine some representative instability scenarios of the multi-ring dynamics including breakup and reconnections, as well as the transient formation of vortex lines.Comment: 10 pages, 8 figure

A chemical imaging and Nano-ARPES study of well-ordered thermally reduced SrTiO3(100)

The structural and electronic properties of thermally reduced SrTiO3(100) single crystals have been investigated using a probe with real- and reciprocal-space sensitivity: a synchrotron radiation microsopic setup which offers the possibility of Scanning Photoemission Microscopy and Angle Resolved Photoelectron Spectroscopy (ARPES) down to the nanometric scale. We have spectroscopically imaged the chemical composition of samples which present reproducible and suitable low-energy electron diffraction patterns after following well-established thermal reduction protocols. At the micrometric scale, Ca-rich areas have been directly imaged using high-energy resolution core level photoemission. Moreover, we have monitored the effect of Ca segregation on different features of the SrTiO3(100) electronic band structure, measuring ARPES inside, outside and at the interface of surface inhomogeneities with the identified Ca-rich areas. In particular, the interaction of Ca with the well-known intragap localized state, previously attributed to oxygen vacancies, has been investigated. Moreover, the combination of direct imaging and spectroscopic techniques with high spatial resolution has clarified the long-standing dilemma related to the bulk or surface character of Ca segregation in SrTiO3. Our results present solid evidence that the penetration depth of Ca segregation is very small. In contrast to what has been previously proposed, the origin of long-range surface reconstructions can unlikely be associated to Ca due to strong local variations of its surface concentration.Comment: 7 pages, 6 figure