Magnetic evanescent-wave Johnson noise from BCS superconductors*

There is evanescent-wave Johnson noise in the vicinity of metallic elements in qubit devices that contributes to qubit decoherence. This noise depends on the dielectric function of the metal, so it changes rather abruptly as the metal becomes superconducting.  We use the BCS form for the wave-vector- and frequency-dependent response function to compute the magnetic noise near the surface of a superconducting half space.  The calculations take the non-locality of the response fully into account.  We present T₁ for a spin qubit, finding a non-monotonic dependence of T₁ on temperature. This effect depends on the impurity density of the superconductor. We also present T₁ as a function of distance from the surface and as a function of qubit frequency. The results suggest that a spin qubit such as an NV center could be used as a probe of the properties of superconducting devices. Additionally, they describe the conditions when superconducting elements can either enhance or mitigate qubit decoherence.