Spin bath-mediated decoherence in superconductors

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We consider a SQUID tunneling between 2 nearly degenerate flux states. Decoherence caused by paramagnetic and nuclear spins in the low-T limit is shown to be much stronger than that from electronic excitations. The decoherence time τϕ is determined by the linewidth Eₒ of spin bath states, which can be reduced by a correct choice of ring geometry and isotopic purification. Eₒ can be measured in either field sweep or microwave absorption experiments, allowing both a test of the theory and design control.