Decoherence and radiation-free relaxation in Meissner transmon qubit coupled to Abrikosov vortices

We present a type of transmon split-junction qubit which can be tuned by Meissner screening currents flowing in the adjacent superconducting film electrodes. The best detected relaxation time (T-1) was of the order of 50 mu s and the dephasing time (T-2) about 40 mu s. The achieved period of oscillation with magnetic field was much smaller than in the usual SQUID-based transmon qubits; thus a strong effective field amplification has been realized. This Meissner qubit allows a strong mixing of the current flowing in the qubit junctions and the currents generated by the Abrikosov vortices. We present a quantitative analysis of the radiation-free relaxation in qubits coupled to the Abrikosov vortices. The observation of coherent quantum oscillations provides strong evidence that the position of the vortex as well as its velocity do not have to accept exact values but can be smeared in the quantum mechanical sense. The eventual relaxation of such states contributes to an increased relaxation rate of the qubit coupled to vortices. Such relaxation is described using basic notions of the Caldeira-Leggett quantum dissipation theory.