Recent experiments on mesoscopic normal-metal--superconductor heterostructures resolve properties on length scales and at low temperatures such that the temperature is below the Thouless energy $k_B T \le E_{Th}$. We describe the properties of these systems within the framework of quasiclassical many-body techniques. Diffusive and ballistic systems are covered, both in equilibrium and nonequilibrium situations. Thereby we demonstrate the common physical basis of various subtopics.

Wolfgang Belzig Frank K. Wilhelm Christoph Bruder Gerd Schön Andrei D. Zaikin

We investigate the properties of complex mesoscopic superconducting-normal hybrid devices, Andreev-Interferometers in the case, where the current is proped through a superconducting tunneling contact whereas the proximity effect is generated by a transparent SN-interface. We show within the quasiclassical Green's functions technique, how the fundamental SNIS-element of the such structures can be mapped onto an effective S$^\prime$IS-junction, where S$^\prime$ is the proximised material with an effective energy gap $E_g<\Delta$. We propose the Andreev-Interferometer, where $E_g$ can be tuned by an external phase $\phi$ and displays maxima at 0 mod $2\pi$ and minima at $\pi$ mod $2\pi$. This leads to peculiar current-phase-relations We propose an experiment to verify our predictions and show, how our results are consistent with recent, unexplained experimental results.

F. K. Wilhelm A. A. Golubov

We study a realistic model for driven qubits using the numerical solution of the Bloch-Redfield equation as well as analytical approximations using a high-frequency scheme. Unlike in idealized rotating-wave models suitable for NMR or quantum optics, we study a driving term which neither is orthogonal to the static term nor leaves the adiabatic energy value constant. We investigate the underlying dynamics and analyze the spectroscopy peaks obtained in recent experiments. We show, that unlike in the rotating-wave case, this system exhibits nonlinear driving effects.We study the width of spectroscopy peaks and show, how a full analysis of the parameters of the system can be performed by comparing the first and second resonance. We outline the limitations of the NMR linewidth formula at low temperature and show, that spectrocopic peaks experience a strong shift which goes much beyond the Bloch-Siegert shift of the Eigenfrequency.

M. C. Goorden F. K. Wilhelm

A measurement on a macroscopic quantum system does in general not lead to a projection of the wavefunction in the basis of the detector as predicted by von-Neumann's postulate. Hence, it is a question of fundametal interest, how the preferred basis onto which the state is projected is selected out of the macroscopic Hilbert space of the system. Detector-dominated von-Neumann measurements are also desirable for both quantum computation and verification of quantum mechanics on a macroscopic scale. The connection of these questions to the predictions of the spin-boson modelis outlined. I propose a measurement strategy, which uses the entanglement of the qubit with a weakly damped harmonic oscillator. It is shown, that the degree of entanglement controls the degree of renormalization of the qubit and identify, that this is equivalent to the degree to which the measurement is detector-dominated. This measurement very rapidly decoheres the initial state, but the thermalization is slow. The implementation in Josephson quantum bits is described and it is shown that this strategy also has practical advantages for the experimental implementation.

F. K. Wilhelm

In the spin-boson model, the properties of the oscillator bath are fully characterized by the spectral density of oscillators $J(\omega)$. We study the case when this function is of Breit-Wigner shape and has a sharp peak at a frequency $\Omega$ with width $\Gamma\ll\Omega$. We use a number of approaches such as the weak-coupling Bloch-Redfield equation, the non-interacting blip approximation (NIBA) and the flow-equation renormalization scheme. We show, that if $\Omega$ is much larger than the qubit energy scales, the dynamics corresponds to an Ohmic spin-boson model with a strongly reduced tunnel splitting. We also show that the direction of the scaling of the tunnel splitting changes sign when the bare splitting crosses $\Omega$. We find good agreement between our analytical approximations and numerical results. We illuminate how and why different approaches to the model account for these features and discuss the interpretation of this model in the context of an application to quantum computation and read-out.

F. K. Wilhelm S. Kleff J. von Delft

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.

P. Rebentrost I. Serban T. Schulte-Herbrueggen F. K. Wilhelm

We propose a detector of microwave photons which can distinguish the vacuum state, one-photon state, and the states with two or more photons. Its operation is based on the two-photon transition in a biased Josephson junction and detection occurs when it switches from a superconducting to a normal state. We model the detector theoretically. The detector performs with more than 90% success probability in several microseconds. It is sensitive for the 8.2GHz photons. The working frequency could be set at the design stage in the range from about 1GHz to 20GHz.

Andrii M. Sokolov Frank K. Wilhelm

We analyze the decoherence of charge states in double quantum dots due to cotunneling. The system is treated using the Bloch-Redfield generalized master equation for the Schrieffer-Wolff transformed Hamiltonian. We show that the decoherence, characterized through a relaxation $\tau_{r}$ and a dephasing time $\tau_{\phi}$, can be controlled through the external voltage and that the optimum point, where these times are maximum, is not necessarily in equilibrium. We outline the mechanism of this nonequilibrium-induced enhancement of lifetime and coherence. We discuss the relevance of our results for recent charge qubit experiments.

Udo Hartmann Frank K. Wilhelm

We perform a nonperturbative analysis of a charge qubit in a double quantum dot structure coupled to its detector. We show that strong detector-dot interaction tends to slow down and halt coherent oscillations. The transitions to a classical and a low-temperature quantum overdamping (Zeno) regime are studied. In the latter, the physics of the dissipative phase transition competes with the effective shot noise.

Udo Hartmann Frank K. Wilhelm

We study noise and noise energy of a high-T$_c$ dc SQUID fabricated on a high-$\epsilon_R$ substrate whose conduction properties are given by transmission line physics. We show that transmission line resonances greatly enhance the noise. Remarkably, resistance asymmetry enhances these resonances even more. However, as the transfer function scales the same way, the noise energy is reduced by asymmetry greatly enhancing the flexibility and performance of the SQUID.

Urbasi Sinha Aninda Sinha Frank K. Wilhelm