Spectroscopic resonance broadening in a Josephson junction qubit due to current noise
Haitan Xu, A. J. Berkley, Roberto Ramos, M. A. Gubrud, Philip R. S. Johnson, Frederick W. Strauch, Alex J. Dragt, J. R. Anderson, Christopher J. Lobb, F. C. Wellstood · Physical Review B · 2005
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 ${f}_{c}⪢{(2\ensuremath{\pi}{T}_{1})}^{\ensuremath{-}1}$, we find that the resonance broadening is proportional to the noise spectral density, while for ${f}_{c}⪡{(2\ensuremath{\pi}{T}_{1})}^{\ensuremath{-}1}$, the broadening is proportional to the rms current noise. We compare our results to microwave spectroscopy data on $100\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}{\mathrm{m}}^{2}$ Nb and Al tunnel junctions at milli-Kelvin temperatures and find good agreement between the measured response spectra and our model simulations.