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 $T_2^{*}$ as a function of the energy relaxation time $T_1$ and the current noise power spectral density. For current noise with a constant spectral density up to a frequency $f_c⪢{\left(2\pi T_1\right)}^{-1}$, we find that the resonance broadening is proportional to the noise spectral density, while for $f_c⪡{\left(2\pi T_1\right)}^{-1}$, the broadening is proportional to the rms current noise. We compare our results to microwave spectroscopy data on $100\mu {\mathrm{m}}^2$ Nb and Al tunnel junctions at milli-Kelvin temperatures and find good agreement between the measured response spectra and our model simulations.

• Received 21 June 2004

DOI:https://doi.org/10.1103/PhysRevB.71.064512