Exact decoherence dynamics of $1\mathrm{/}f$ noise

In this paper, we investigate the exact decoherence dynamics of a superconducting resonator coupled to an electromagnetic reservoir characterized by the $1\mathrm{/}f$ noise at finite temperature, where a full quantum description of the environment with $1\mathrm{/}{f}^x$ noise (with $x\approx 1$) is presented. The exact master equation and the associated non-equilibrium Green’s functions are solved exactly for such an open system. We show a clear signal of non-Markovian dynamics induced purely by $1\mathrm{/}f$ noise. Our analysis is also applicable to another nano/micro mechanical oscillators. Finally, we demonstrate the non-Markovian decoherence dynamics of photon number superposition states using Wigner distribution that could be measured in experiments.