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- Condensed Matter Physics
- Mathematical Physics
- Quantum Field Theory and Strings
- Computational Physics
- Particle Physics
- Quantum Information Theory

# Projects

# Main content

### Mesoscopic Systems

Our research focuses on the design and functionality of mesoscopic solid state devices, their transport and noise properties, and their potential use in quantum information theory. We have suggested specific mesoscopic structures allowing for the study of basic quantum phenomena such as entanglement and wave function collapse. We have shown how to test for the non-classical correlations through the use of a Bell inequality test based on current-current cross correlators. We have suggested a design for a solid-state entangler using a normal-metal--superconductor junction injecting entangled pairs of quasi-particles into a normal-metal lead. Here, the quantum correlated two-particle states arise from Cooper pairs decaying into the normal lead and are characterized by entangled spin- and orbital degrees of freedom. In an alternative setup with a normal-metal device in a fork geometry the entanglement is produced via postselection in the measurement process (non-interacting limit). Both, the dc and pulsed production of entangled pairs has been analyzed. In our recent work we have unveiled the relation between the fidelity (stability under perturbation) of a quantum system and the generating function of full counting statistics and have analyzed the possibility of their measurement using a quantum bit as a measurement device.

### Quantum Computing

In a quantum computer the information is stored in arrays of quantum two-level systems; these qubits generalize the notion of the well known bit in a classical computer. Execution of a quantum algorithm involves quantum gates, unitary operations rotating individual qubits and entangling them pairwise. Superconducting solid-state qubits are promising candidates for the hardware implementation of scalable quantum information processors; quantum fluctuations are introduced through small-capacitance Josephson junctions and the frustrating drive is introduced through a gate potential (charge-qubit) or a magnetic flux (phase- or flux qubit). We have proposed various designs for the solid-state implementation of qubits based on superconducting structures: We have shown how to build a quiet qubit using superconductors with d-wave symmetry and have suggested a first design for topological computing based on a quantum Josephson junction array. In our most recent proposal we suggest to exploit the symmetry properties of a tetrahedral structure (four equal islands with pairwise symmetric coupling) in order to emulate a spin-1/2 system in zero field with quadratic noise stability and generically large quantum fluctuations, an ideal starting point for a qubit. We have investigated a generic decoherence channel in superconducting qubits which is due to phonon radiation in the Josephson junctions arising from the piezoelectric coupling between the dynamic superconducting phase and the junction insulator. Our recent interest is in the further understanding and development of the tetrahedral qubit, in particular the effect of (weak) symmetry breaking on its properties and the implementation of simple experiments testing the coherent operation of the device.

### Quantum Coherent Atomic Gases

Cooling atoms to the nano-Kelvin regime allows for the realization and study of new thermodynamic phase transitions and their associated phases, with an interesting synergy emerging between the fields of quantum atom optics and condensed matter physics. Topics of interest are the study of the superfluid to Mott-insulator phase transition appearing in cold bosonic systems subject to an optical lattice, the striving for the realization of a BCS-type condensate in a fermionic system, the investigation of effects due to disorder and reduced dimensionality, the proposal and implementation of novel quantum phases and associated transitions, etc. We have studied the instability towards the Mott insulator appearing in one-dimensional confined Bose gases, the appearance of a supersolid phase in two-dimensional mixed Fermion-Boson systems, the instability towards phase separation, and the implementation of a ring-exchange term with quantum optical means leading to a lattice gauge theory. In our recent work, we study the dynamic properties of the Bose-Hubbard model in the vicinity of the Mott-insulator to superfluid phase transition. We determine the excitations over a mean-field groundstate within a truncated Hilbert space and analyze the evolution of the spectrum across the transition. The determination of the system response to various external drives allows for the experimental verification of our results.

### Statistical Physics

Disordered systems exhibit interesting thermodynamic and nonequilibrium properties relevant to the functionality of magnetic and superconducting systems. We have studied dirty elastic manifolds in the context of vortex matter physics and the properties of various types of glasses, such as spin, structural, and gauge glasses. Questions of interest are the basic understanding of the glass phase (droplet picture versus replica symmetry breaking, structural properties of the vortex glass phase), the thermodynamic properties of the glass transition (e.g., scaling laws and universality, entropy crisis in structural glasses), and the influence of thermal and quantum fluctuations on the response properties of a glass (creep dynamics). We make use of various analytical (replica approach, instantons, functional renormalization group) and numerical techniques (parallel tempering Monte Carlo and cluster algorithms). Recent interest is in the analytical description of the glass transition in a model liquid, the exact solution of the 1+1-dimensional random polymer problem, and the absence of the Almeida-Thouless line in 3D short-range spin glasses.

### Vortices in Type II Superconductors

We have contributed to the development of the new Vortex Matter phenomenology in disordered and strongly fluctuating type II superconductors: Particular research topics studied in the past are the theory of classical and quantum creep of vortices, classical and quantum melting, the decoupling transition in layered systems, anisotropic scaling theory, quantum depinning, weak collective pinning and functional renormalization group theory, strong pinning, correlated disorder, vortex dynamics, Hall effect, vortex charge, the van der Waals attraction between vortices, the structure of vortices in d-wave superconductors, and the electronic structure and dissipation in moderately clean superconductors. Recent reserach efforts concentrate on the phenomenon of strong pinning and its crossover to the weak collective pinning scenario, the zero-field superconductor to normal transition in bi- and multilayer systems, the density functional theory of bulk and surface melting of the pancake-vortex lattice in layered superconductors.

**Literature:**

[1] G. Blatter, M.V. Feigel'man, V.B. Geshkenbein, A.I. Larkin, and V.M. Vinokur, Vortices in high temperature superconductors, Rev. Mod. Phys. 66, 1125 (1994).

[2] G. Blatter and V.B. Geshkenbein, Vortex Matter, The Physics of Superconductors, Vol. 1, Conventional and High-Tc superconductors, eds. K.H. Bennemann and J.B. Ketterson (Springer, Berlin, 2003), pp 726.