Exact decoherence dynamics of $1/f$ noise

TL;DR

This paper provides an exact quantum analysis of decoherence caused by $1/f$ noise in superconducting resonators, revealing non-Markovian effects and offering insights applicable to nano/micro mechanical oscillators.

Contribution

It presents an exact solution for the decoherence dynamics under $1/f$ noise, including the master equation and Green's functions, highlighting non-Markovian behavior.

Findings

Non-Markovian dynamics induced by $1/f$ noise.

Exact master equation and Green's functions derived.

Non-Markovian decoherence of photon superposition states demonstrated.

Abstract

In this paper, we investigate the exact decoherence dynamics of a superconducting resonator coupled to an electromagnetic reservoir characterized by the $1/f$ noise at finite temperature, where a full quantum description of the environment with $1/f^{x}$ 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 $1/f$ 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.