Optimal control of a leaking qubit

Physical implementations of quantum bits can contain coherent transitions to energetically close non-qubit states. In particular, for anharmonic oscillator systems such as the superconducting phase qubit and the transmon a two-level approximation is insufficient. We apply optimal control theory to the envelope of a resonant Rabi pulse in a qubit in the presence of a single, weakly off-resonant leakage level. The gate error of a spin flip operation reduces by orders of magnitude compared to simple pulse shapes. Near-perfect gates can be achieved for any pulse duration longer than an intrinsic limit given by the nonlinearity. The pulses can be understood as composite sequences that refocus the leakage transition. We also discuss ways to improve the pulse shapes.Comment: 4 pages, 2 figure

Optimal control of a qubit coupled to a non-Markovian environment

A central challenge for implementing quantum computing in the solid state is decoupling the qubits from the intrinsic noise of the material. We investigate the implementation of quantum gates for a paradigmatic, non-Markovian model: A single qubit coupled to a two-level system that is exposed to a heat bath. We systematically search for optimal pulses using a generalization of the novel open systems Gradient Ascent Pulse Engineering (GRAPE) algorithm. We show and explain that next to the known optimal bias point of this model, there are optimal shapes which refocus unwanted terms in the Hamiltonian. We study the limitations of controls set by the decoherence properties. This can lead to a significant improvement of quantum operations in hostile environments.Comment: 5 pages, 3 figures, improved pulse shape

Decoherence of a two-qubit system with a variable bath coupling operator

We examine the decoherence of an asymmetric two-qubit system that is coupled via a tunable interaction term to a common bath or two individual baths of harmonic oscillators. The dissipative dynamics are evaluated using the Bloch-Redfield formalism. It is shown that the behaviour of the decoherence effects is affected mostly by different symmetries between the qubit operator which is coupled to the environment and temperature, whereas the differences between the two bath configurations are very small. Moreover, it is elaborated that small imperfections of the qubit parameters do not lead to a drastic enhancement of the decoherence rates.Comment: 10 pages, 5 figure

Transient dynamics of a superconducting nonlinear oscillator

We investigate the transient dynamics of a lumped-element oscillator based on a dc superconducting quantum interference device (SQUID). The SQUID is shunted with a capacitor forming a nonlinear oscillator with resonance frequency in the range of several GHz. The resonance frequency is varied by tuning the Josephson inductance of the SQUID with on-chip flux lines. We report measurements of decaying oscillations in the time domain following a brief excitation with a microwave pulse. The nonlinearity of the SQUID oscillator is probed by observing the ringdown response for different excitation amplitudes while the SQUID potential is varied by adjusting the flux bias. Simulations are performed on a model circuit by numerically solving the corresponding Langevin equations incorporating the SQUID potential at the experimental temperature and using parameters obtained from separate measurements characterizing the SQUID oscillator. Simulations are in good agreement with the experimental observations of the ringdowns as a function of applied magnetic flux and pulse amplitude. We observe a crossover between the occurrence of ringdowns close to resonance and adiabatic following at larger detuning from the resonance. We also discuss the occurrence of phase jumps at large amplitude drive. Finally, we briefly outline prospects for a readout scheme for superconducting flux qubits based on the discrimination between ringdown signals for different levels of magnetic flux coupled to the SQUID.Comment: 15 pages, 9 figure

Stereoscopic Polar Plume Reconstructions from Stereo/Secchi Images

We present stereoscopic reconstructions of the location and inclination of polar plumes of two data sets based on the two simultaneously recorded images taken by the EUVI telescopes in the SECCHI instrument package onboard the \emph{STEREO (Solar TErrestrial RElations Observatory)} spacecraft. The ten plumes investigated show a superradial expansion in the coronal hole in 3D which is consistent with the 2D results. Their deviations from the local meridian planes are rather small with an average of $6.47^{\circ}$. By comparing the reconstructed plumes with a dipole field with its axis along the solar rotation axis, it is found that plumes are inclined more horizontally than the dipole field. The lower the latitude is, the larger is the deviation from the dipole field. The relationship between plumes and bright points has been investigated and they are not always associated. For the first data set, based on the 3D height of plumes and the electron density derived from SUMER/\emph{SOHO} Si {\sc viii} line pair, we found that electron densities along the plumes decrease with height above the solar surface. The temperature obtained from the density scale height is 1.6 to 1.8 times larger than the temperature obtained from Mg {\sc ix} line ratios. We attribute this discrepancy to a deviation of the electron and the ion temperatures. Finally, we have found that the outflow speeds studied in the O {\sc vi} line in the plumes corrected by the angle between the line of sight and the plume orientation are quite small with a maximum of 10 $\mathrm{km s^{-1}}$. It is unlikely that plumes are a dominant contributor to the fast solar wind.Comment: 25 pages, 13 figure

The Josephson critical current in a long mesoscopic S-N-S junction

We carry out an extensive experimental and theoretical study of the Josephson effect in S-N-S junctions made of a diffusive normal metal (N) embedded between two superconducting electrodes (S). Our experiments are performed on Nb-Cu-Nb junctions with highly-transparent interfaces. We give the predictions of the quasiclassical theory in various regimes on a precise and quantitative level. We describe the crossover between the short and the long junction regimes and provide the temperature dependence of the critical current using dimensionless units $eR_{N}I_{c}/\epsilon_{c}$ and $k_{B}T/\epsilon_{c}$ where $\epsilon_{c}$ is the Thouless energy. Experimental and theoretical results are in excellent quantitative agreement.Comment: 5 pages, 4 figures, slighly modified version, publishe

Phase Transition in a Stochastic Forest Fire Model and Effects of the Definition of Neighbourhood

We present results on a stochastic forest fire model, where the influence of the neighbour trees is treated in a more realistic way than usual and the definition of neighbourhood can be tuned by an additional parameter. This model exhibits a surprisingly sharp phase transition which can be shifted by redefinition of neighbourhood. The results can also be interpreted in terms of disease-spreading and are quite unsettling from the epidemologist's point of view, since variation of one crucial parameter only by a few percent can result in the change from endemic to epidemic behaviour.Comment: 23 pages, 13 figure