Uta Naether

Peierls-Nabarro energy surfaces and directional mobility of discrete solitons in two-dimensional saturable nonlinear Schrodinger lattices

We address the problem of directional mobility of discrete solitons in two-dimensional rectangular lattices, in the framework of a discrete nonlinear Schrödinger model with saturable on-site nonlinearity. A numerical constrained Newton-Raphson method is used to calculate two-dimensional Peierls-Nabarro energy surfaces, which describe a pseudopotential landscape for the slow mobility of coherent localized excitations, corresponding to continuous phase-space trajectories passing close to stationary modes. Investigating the two-parameter space of the model through independent variations of the nonlinearity constant and the power, we show how parameter regimes and directions of good mobility are connected to the existence of smooth surfaces connecting the stationary states. In particular, directions where solutions can move with minimum radiation can be predicted from flatter parts of the surfaces. For such mobile solutions, slight perturbations in the transverse direction yield additional transverse oscillations with frequencies determined by the curvature of the energy surfaces, and with amplitudes that for certain velocities may grow rapidly. We also describe how the mobility properties and surface topologies are affected by inclusion of weak lattice anisotropy.

Compactification tuning for nonlinear localized modes in sawtooth lattices.

We discuss the properties of nonlinear localized modes in sawtooth lattices, in the framework of a discrete nonlinear Schrödinger model with general on-site nonlinearity. Analytic conditions for existence of exact compact three-site solutions are obtained, and explicitly illustrated for the cases of power-law (cubic) and saturable nonlinearities. These nonlinear compact modes appear as continuations of linear compact modes belonging to a flat dispersion band. While for the linear system a compact mode exists only for one specific ratio of the two different coupling constants, nonlinearity may lead to compactification of otherwise noncompact localized modes for a range of coupling ratios, at some specific power. For saturable lattices, the compactification power can be tuned by also varying the nonlinear parameter. Introducing different on-site energies and anisotropic couplings yields further possibilities for compactness tuning. The properties of strongly localized modes are investigated numerically for cubic and saturable nonlinearities, and in particular their stability over large parameter regimes is shown. Since the linear flat band is isolated, its compact modes may be continued into compact nonlinear modes both for focusing and defocusing nonlinearities. Results are discussed in relation to recent realizations of sawtooth photonic lattices.

Nanoscale constrictions in superconducting coplanar waveguide resonators

We report on the design, fabrication, and characterization of superconducting coplanar waveguide resonators with nanoscopic constrictions. By reducing the size of the center line down to 50 nm, the radio frequency currents are concentrated and the magnetic field in its vicinity is increased. The device characteristics are only slightly modified by the constrictions, with changes in resonance frequency lower than 1% and internal quality factors of the same order of magnitude as the original ones. These devices could enable the achievement of higher couplings to small magnetic samples or even to single molecular spins and have applications in circuit quantum electrodynamics, quantum computing, and electron paramagnetic resonance.

From Josephson junction metamaterials to tunable pseudo-cavities

The scattering through a Josephson junction (JJ) interrupting a superconducting line is revisited including power leakage. We also discuss how to make tunable and broadband resonant mirrors by concatenating junctions. As an application, we show how to construct cavities using these mirrors, thus connecting two research fields: JJ quantum metamaterials and coupled-cavity arrays. We finish by discussing the first nonlinear corrections to the scattering and their measurable effects.

Stationary discrete solitons in a driven dissipative Bose-Hubbard chain

We demonstrate that stationary localized solutions (discrete solitons) exist in a one dimensional Bose-Hubbard lattices with gain and loss in the semiclassical regime. Stationary solutions, by defi- nition, are robust and do not demand for state preparation. Losses, unavoidable in experiments, are not a drawback, but a necessary ingredient for these modes to exist. The semiclassical calculations are complemented with their classical limit and dynamics based on a Gutzwiller Ansatz. We argue that circuit QED architectures are ideal platforms for realizing the physics developed here. Finally, within the input-output formalism, we explain how to experimentally access the different phases, including the solitons, of the chain.

Quantum Chaos in an Ultrastrongly Coupled Bosonic Junction

The semiclassical and quantum dynamics of two ultrastrongly coupled nonlinear resonators cannot be explained using the discrete nonlinear Schrödinger equation or the Bose-Hubbard model, respectively. Instead, a model beyond the rotating wave approximation must be studied. In the semiclassical limit this model is not integrable and becomes chaotic for a finite window of parameters. For the quantum dimer we find corresponding regions of stability and chaos. The more striking consequence for both semiclassical and quantum chaos is that the tunneling time between the sites becomes unpredictable. These results, including the transition to chaos, can be tested in experiments with superconducting microwave resonators.

Stationary discrete solitons in circuit QED

We demonstrate that stationary localized solutions (discrete solitons) exist in a one dimensional Bose-Hubbard lattices with gain and loss in the semiclassical regime. Stationary solutions, by defi- nition, are robust and do not demand for state preparation. Losses, unavoidable in experiments, are not a drawback, but a necessary ingredient for these modes to exist. The semiclassical calculations are complemented with their classical limit and dynamics based on a Gutzwiller Ansatz. We argue that circuit QED architectures are ideal platforms for realizing the physics developed here. Finally, within the input-output formalism, we explain how to experimentally access the different phases, including the solitons, of the chain.

The Bose-Hubbard model with squeezed dissipation

The stationary properties of the Bose-Hubbard model under squeezed dissipation are investigated. The dissipative model does not possess a

Multistable regime and intermediate solutions in a nonlinear saturable coupler

U(1)

Pseudo-two-dimensional random dimer lattices

symmetry, but parity is conserved: