# Dresden 2009 – wissenschaftliches Programm

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# TT: Fachverband Tiefe Temperaturen

## TT 13: Focussed Session: Superconducting Quantum Circuits

### TT 13.3: Topical Talk

### Dienstag, 24. März 2009, 10:30–11:00, HSZ 03

**Landau-Zener Transitions in Qubit-Oscillator Settings** — •Sigmund Kohler — Institut für Physik, Universität Augsburg, 86135 Augsburg

The coupling between a qubit and a mode of a transmission line induces Landau-Zener transitions of the qubit upon switching the gate voltage or the magnetic flux that penetrates the superconducting loop. The adiabatic energies of this system are characterized by multiple exact and avoided level crossings for which the usual two-level Landau-Zener formula is no longer applicable. We derive selection rules for the multi-level transitions and present an exact expression for the corresponding transition probabilities [1,2]. Applications include quantum state preparation like single-photon generation and the controllable creation of qubit-oscillator entanglement. If the circuit is driven by a rf signal, the phase of the reflected signal depends on the state of the qubit. We discuss the possibility of monitoring Landau-Zener transitions in that way. A natural generalization addresses the coupling of the qubit to a bath of harmonic oscillator. This defines the dissipative Landau-Zener problem which recently gained interest in the context of adiabatic quantum computation. We derived an exact solution of this problem in the zero-temperature limit [3].

[1] K. Saito *et al.*. Europhys. Lett. **76**, 22 (2006).

[2] D. Zueco, P. Hänggi, and S. Kohler, New. J. Phys. **10**, 115012 (2008).

[3] M. Wubs *et al.*, Phys. Rev. Lett. **97**, 200404 (2006).