Yu. Makhlin 1,2, G. Schön 1,3, and A. Shnirman 1
1Institut für Theoretische Festkörperphysik, Universität Karlsruhe, D-76128 Karlsruhe, Germany
2Landau Institute for Theoretical Physics, Kosygin St. 2, 117940 Moscow, Russia
3Institut für Nanotechnologie, Forschungszentrum Karlsruhe, D-76021 Karlsruhe, Germany

Dissipative effects in Josephson qubits

Chem. Phys. 296, 315-324 (2004)
Special Issue on The spin boson problem: from electron transfer to quantum computing, eds. H. Grabert and A. Nitzan

Josephson-junction systems have been studied as potential realizations of quantum bits. For their operation as qubits it is crucial to maintain quantum phase coherence for long times. Frequently relaxation and dephasing effects are described in the frame of the Bloch equations. Recent experiments demonstrate the importance of 1/f noise, or operate at points where the linear coupling to noise sources is suppressed. This requires generalizations and extensions of known methods and results. In this tutorial we present the Hamiltonian for Josephson qubits in a dissipative environment and review the derivation of the Bloch equations as well as systematic generalizations. We discuss 1/f noise, nonlinear coupling to the noise source, and effects of strong pulses on the dissipative dynamics. The examples illustrate the renormalization of qubit parameters by the high-frequency noise spectrum as well as non-exponential decay governed by low-frequency modes.