Spectroscopic resonance broadening in a Josephson junction qubit due to current noise

We analyze the effect of dissipation and low-frequency current noise on quantum coherence in a current-biased Josephson junction that has low damping. Developing a stochastic Bloch equation for the reduced density matrix of the system, we determine the resonance response of the system to a weak external microwave current drive. We characterize the response by finding the spectroscopic coherence time T₂^* as a function of the energy relaxation time T₁ and the current noise power spectral density. For current noise with a constant spectral density up to a frequency f_c⪢(2πT₁)⁻¹, we find that the resonance broadening is proportional to the noise spectral density, while for f_c⪡(2πT₁)⁻¹, the broadening is proportional to the rms current noise. We compare our results to microwave spectroscopy data on 100 μm² Nb and Al tunnel junctions at milli-Kelvin temperatures and find good agreement between the measured response spectra and our model simulations.