Evanescent-wave Johnson noise from BCS superconductors

Qubits near conducting devices are susceptible to decoherence due to electromagnetic field fluctuations, which leak from the devices as evanescent-wave Johnson noise. An interesting question is to what extent these fluctuations change when the metal becomes superconducting. This noise depends on the electromagnetic response function, which for BCS superconductors has been well studied for arbitrary impurity density. We use this response function to calculate the noise outside the surface of a superconducting half-space in thermodynamic equilibrium. We present T₁ of a qubit as a function of temperature, qubit frequency, and distance from the surface. This enables us to characterize the transition from the normal to the superconducting state and we find that the surface-wave contribution is greater in the superconductor. In many experiments a superconducting device element is out of equilibrium due to quasiparticle poisoning, and we also investigate this case. The results show how to use charge or spin qubits as probes of superconducting devices, and they can serve as guides in the design of qubit device architectures.