We demonstrate experimentally the existence of a continuous phase transition between a normal and a true superconductiug phase (with zero linear resistivity) in epitaxial films of Y-Ba-Cu-0 in strong magnetic fields, H&&H, I. The nonlinear I-V curves show scaling behavior near the transition and the relevant critical exponents are extracted. These exponents are consistent with values expected for freezing into a superconducting vortex-glass phase.

We present a multi-level quantum theory of decoherence for a general circuit realization of a superconducting qubit. Using electrical network graph theory, we derive a Hamiltonian for the circuit. The dissipative circuit elements (external impedances, shunt resistors) are described using the Caldeira-Leggett model. The master equation for the superconducting phases in the Born-Markov approximation is derived and brought into the Bloch-Redfield form in order to describe multi-level dissipative quantum dynamics of the circuit. The model takes into account leakage effects, i.e. transitions from the allowed qubit states to higher excited states of the system. As a special case, we truncate the Hilbert space and derive a two-level (Bloch) theory with characteristic relaxation (T1) and decoherence (T2) times. We apply our theory to the class of superconducting flux qubits; however, the formalism can be applied for both superconducting flux and charge qubits.

We propose a model for 1/f flux noise in superconducting devices (f is frequency). The noise is generated by the magnetic moments of electrons in defect states which they occupy for a wide distribution of times before escaping. A trapped electron occupies one of the two Kramers-degenerate ground states, between which the transition rate is negligible at low temperature. As a result, the magnetic moment orientation is locked. Simulations of the noise produced by randomly oriented defects with a density of 5 × 10 17 m -2 yield 1/f noise magnitudes in good agreement with experiments.

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