Superconducting quantum circuits are among the most promising solid state candidates as building elements for quantum computers due to their ultra-low dissipation, inherent to superconductors.

In general, superconducting quantum devices have unique properties like magnetic field resolution, coherence, scalability, and implementation. They are well suited for applications ranging from basic research over to applied disciplines like material characterization, medical imaging to quantum computers. Superconducting qubits fulfill the DiVincenzo criteria for a scalable quantum computer. Using integrated-circuit processing techniques such as used for digital and rapid single flux quantum (RSFQ) circuits, complex micron-sized quantum circuits can be scaled up to a large number of qubits.

In ten years, impressive progress has been made to address, control, readout, and scale superconducting qubits, resulting, for example, in the proof of the violation of Bell's inequality, measurements of three qubit entanglement, quantum non-demolition readout, creation of arbitrary photon states, and circuit quantum electrodynamics in strong and ultra-strong coupling regimes.

At KIT, we simulate, design, fabricate and measure **superconducting qubits** - including varieties of **phase, flux and transmon qubits**. The qubits are controlled by DC flux to chance their level splitting (|0> and |1> state) and by microwave pulses to excite them. As the typical energy splitting between the qubit states is about several GHz, the temperature of the circuit has to be kept low enough (10 GHz <-> 0.5 K) to avoid thermal population of the excited states.

**Our research interests range from new readout techniques, qubit designs, resonant circuit material science to quantum metamaterials and quantum simulation**.Starting from circuit simulation we implement the quantum chips using local facilities (Center for Functional Nanostructures) before measuring in a dilution refrigerator.

**Students **are always welcome for** Bachelor, Master or PhD positions**. We use** quantum and electromagnetic circuit simulation, nanotechnology, milliKelvin cryostats, and transport and microwave setups** for our research. The projects depend on the current state of our research. In case you are interested please please feel free to contact us.

Contact: Dr. Martin Weides

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Soliton propagation is an interesting field in various contexts within nonlinear physics.

A unique feature of long Josephson junctions is that they allow the experimental study of soliton dynamics with a great degree of precision, impossible for many other physical systems with solitons.

A soliton in a Josephson junction accounts for a magnetic flux quantum moving between two superconducting electrodes. Mathematically, it is described by a solitarywave solution of the sine-Gordon equation which models the electromagnetic wave propagation in the junction.v

A soliton in a Josephson junction accounts for a magnetic flux quantum moving between two superconducting electrodes. Mathematically, it is described by a solitarywave solution of the sine-Gordon equation which models the electromagnetic wave propagation in the junction.

When increasing the bias current, the soliton velocity increases and approaches the velocity of light in the junction (so-called Swihart velocity). This velocity is about 30 times smaller than the light velocity in vacuum. The soliton has all characteristic properties of a relativistic particle. Thus, here we can experimentally study the relativistic dynamics in a volume of less than 1 cm^{3}!

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The superconducting state has unique features for realizing compact solid-state devices with controllable macroscopic quantum properties and long coherence time.

Investigation of intrinsic origins of the nonlinear behavior and energy losses in superconducting structures at microwave frequencies has both fundamental and practical relevance. In particular, it is important to identify the local sources of nonlinearity associated with the global nonlinear response of superconducting structures irradiated by microwaves.

We apply a high-resolution, nondestructive evaluation technique of low-temperature laser scanning microscopy to the investigation of local microwave properties of superconducting thin-film circuits. In this technique, a modulated laser beam is focused onto and scanned over the surface of a resonant superconducting device to probe the spatial distribution of microwave currents.

The spatially localized photo-induced change of the kinetic inductance of the device produces both a shift of the resonant frequency and change of the quality factor. An image of these changes is recorded as the laser spot is scanned over the device. By using a newly developed procedure of spatially-resolved wave impedance partition, the influence of inhomogeneous current flow on the formation of nonlinear microwave response in such planar devices is analyzed in terms of the independent impact from resistive and inductive components. The capability of our method to probe the spatial variations of two-tone, third-order intermodulation currents on micron length scales is used to find the 2D distribution of the local sources of nonlinear response.

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Nonlinearity and lattice discreteness of many nonlinear lattices lead to a generic class of excitations that are spatially localized on the scale comparable to the lattice constant. These excitations, also known as intrinsic localized modes or discrete breathers, have recently attracted a lot of interest in theory of nonlinear lattices.

The energy of a breather is strongly localized in one place and does not diffuse to other regions of the system. A characteristic property of discrete breathers in dissipative systems is that these localized excitations are predicted to persist under the influence of a spatially uniform driving force. Discrete breathers have been discussed in connection with a variety of physical systems such as large molecules, molecular crystals, and spin lattices.

Our group pioneered imaging of these localized excitations in (quasi-)2-dimensional arrays of coupled Josephson junctions also called Josephson ladders. A biased Josephson junction behaves very similar to its mechanical analog that is a forced and damped pendulum. An electric bias current flowing across the junction is analogous to a torque applied to the pendulum. The maximum torque that the pendulum can sustain and remain static corresponds to the critical current of the junction. For low damping and bias below the critical current, the junction allows for two states: the superconducting (static) state and the resistive (rotating) state. The phase difference of the macroscopic wave functions of the superconducting islands on both sides of the junction plays the role of an angle coordinate of the pendulum. According to the Josephson relation, a junction in a rotating state generates a dc voltage which can be measured. A discrete breather in a Josephson ladder corresponds to a state where one (or several) junctions are in the whirling (resistive) state, with all other junctions performing small forced oscillations around their stable equilibria.

We use the method of low temperature laser scanning microscopy to visualize various rotating states in our ladders.

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# Research group Ustinov: Hybrid Quantum Systems

Future quantum networks will interconnect many quantum systems of diverse physical nature. Photons are ideal carriers of quantum information over long distances because they can be efficiently send through low loss optical fibers. On the other hand, fast and scalable quantum gates can be implemented in solid-state system, e.g. architectures involving superconducting circuits. Thus, interfacing photonic and solid-state qubits withing a hybrid quantum architecture offers a promising route towards large scale distributed quantum computing. Ensembles of optically active spins are promising candidates for realizing such a quantum media converter. Among these, spin ensembles consisting of rare earth (RE) erbium Er^{3+} ions doped into a Y_{2}SiO_{5} crystal matrix play a special role due to the 1.54 µm optical transition of Er^{3+}, which exactly matches the low loss Telecom C-band of optical fiber communication.

This project is supported by the "Bundesministerium für Bildung und Forschung" through the project QUIMP.

Contact: Dr. Pavel Bushev, Sebastian Probst

**Spezialvorlesung im Sommersemester 2013:** *"Introduction into Quantum Optics and Quantum Communication"*, Di. 14:00 Uhr, Kleiner Hörsaal A (Geb. 30.22), (Aushang)

**Publications:**

[1] S. Probst, H. Rotzinger, S. Wünsch, P. Jung, M. Jerger, M. Siegel, A. V. Ustinov, P. A. Bushev, *"Anisotropic rare-earth spin ensemble strongly coupled to a superconducting resonator"*, Phys. Rev. Lett. **110**, 157001 (2013) arXiv:1212.2856 [quant-ph]

[2] Matthias U. Staudt, Io-Chun Hoi, Philip Krantz, Martin Sandberg, Michaël Simoen, Pavel Bushev, Nicolas Sangouard, Mikael Afzelius, Vitaly S. Shumeiko, Göran Johansson, *"Coupling of an erbium spin ensemble to a superconducting resonator"*, J. Phys. B: At. Mol. Opt. Phys. **45** 124019 (2012)

[3] P. Bushev, A. K. Feofanov, H. Rotzinger, I. Protopopov, J. H. Cole, C. M. Wilson, G. Fischer, A. Lukashenko and A. V. Ustinov, *"Ultralow-power spectroscopy of a rare-earth spin ensemble using a superconducting resonator"*, Phys. Rev. B **84**, 060501(R) (2011)