Ultrafast current imaging by Bayesian inversion.

Spectroscopic measurements of current-voltage curves in scanning probe microscopy is the earliest and one of the most common methods for characterizing local energy-dependent electronic properties, providing insight into superconductive, semiconductor, and memristive behaviors. However, the quasistatic nature of these measurements renders them extremely slow. Here, we demonstrate a fundamentally new approach for dynamic spectroscopic current imaging via full information capture and Bayesian inference. This general-mode I-V method allows three orders of magnitude faster measurement rates than presently possible. The technique is demonstrated by acquiring I-V curves in ferroelectric nanocapacitors, yielding >100,000 I-V curves in <20 min. This allows detection of switching currents in the nanoscale capacitors, as well as determination of the dielectric constant. These experiments show the potential for the use of full information capture and Bayesian inference toward extracting physics from rapid I-V measurements, and can be used for transport measurements in both atomic force and scanning tunneling microscopy.

Characteristics of two-dimensional quantum turbulence in a compressible superfluid.

Fluids subjected to suitable forcing will exhibit turbulence, with characteristics strongly affected by the fluid's physical properties and dimensionality. In this work, we explore two-dimensional (2D) quantum turbulence in an oblate Bose-Einstein condensate confined to an annular trapping potential. Experimentally, we find conditions for which small-scale stirring of the condensate generates disordered 2D vortex distributions that dissipatively evolve toward persistent currents, indicating energy transport from small to large length scales. Simulations of the experiment reveal spontaneous clustering of same-circulation vortices and an incompressible energy spectrum with k(-5/3) dependence for low wave numbers k. This work links experimentally observed vortex dynamics with signatures of 2D turbulence in a compressible superfluid.

Stable vortex-bright-soliton structures in two-component Bose-Einstein condensates.

We report the numerical realization of robust two-component structures in 2D and 3D Bose-Einstein condensates with nontrivial topological charge in one component. We identify a stable symbiotic state in which a higher-dimensional bright soliton exists even in a homogeneous setting with defocusing interactions, due to the effective potential created by a stable vortex in the other component. The resulting vortex-bright-solitons, generalizations of the recently experimentally observed dark-bright solitons, are found to be very robust both in the homogeneous medium and in the presence of external confinement.

Two-dimensional paradigm for symmetry breaking: the nonlinear Schrödinger equation with a four-well potential.

We study the existence and stability of localized modes in the two-dimensional (2D) nonlinear Schrödinger/Gross-Pitaevskii (NLS/GP) equation with a symmetric four-well potential. Using the corresponding four-mode approximation, we trace the parametric evolution of the trapped stationary modes, starting from the linear limit, and thus derive a complete bifurcation diagram for families of the stationary modes. This provides the picture of spontaneous symmetry breaking in the fundamental 2D setting. In a broad parameter region, the predictions based on the four-mode decomposition are found to be in good agreement with full numerical solutions of the NLS/GP equation. Stability properties of the stationary states coincide with those suggested by the corresponding discrete model in the large-amplitude limit. The dynamics of unstable modes is explored by means of direct simulations. Finally, in addition to the full analysis for the case of the self-attractive nonlinearity, the bifurcation diagram for the case of self-repulsion is briefly considered too.

Discrete solitons and vortices in hexagonal and honeycomb lattices: existence, stability, and dynamics.

We consider a prototypical dynamical lattice model, namely, the discrete nonlinear Schrödinger equation on nonsquare lattice geometries. We present a systematic classification of the solutions that arise in principal six-lattice-site and three-lattice-site contours in the form of both discrete multipole solitons and discrete vortices. Additionally to identifying the possible states, we analytically track their linear stability both qualitatively and quantitatively. We find that among the six-site configurations, the "hexapole" of alternating phases (0-pi) , as well as the vortex of topological charge S=2 have intervals of stability; among three-site states, only the vortex of topological charge S=1 may be stable in the case of focusing nonlinearity. These conclusions are confirmed both for hexagonal and for honeycomb lattices by means of detailed numerical bifurcation analysis of the stationary states from the anticontinuum limit, and by direct simulations to monitor the dynamical instabilities, when the latter arise. The dynamics reveal a wealth of nonlinear behavior resulting not only in single-site solitary wave forms, but also in robust multisite breathing structures.