Non-Gaussian dephasing in flux qubits due to 1/f noise

A remarkable work 1 has appeared recently, reporting on measurements of the two-pulse echo signal in Josephsonjunction flux qubits revealing its dependence of the time interval between the pulses. The authors interpreted their results in terms of the recent theory 2 of the decoherence in qubits caused by 1/f noise and obtained the qubit dephasing rate, , based on the postulation of the Gaussian statistics of the noise. Although this looks like a natural starting point, the importance of the echo signal data for understanding the underlying mechanisms of the qubits, decoherence calls for careful examination of the assumptions built into the theoretical description. In this paper we develop a theory of the time dependence of the echo signal making use of an exactly solvable but experimentally realistic model. We demonstrate that in many practical realizations of 1/f noise the results based on the Gaussian assumption need to be significantly corrected. We show that deviation of noise statistics from the Gaussian changes significantly the time dependence of the echo signal. Using the exactly solvable non-Gaussian spin-fluctuator model for the 1/f noise we analyze the dependence of the echo signal on both time and the qubit working point, and compare the obtained results with those derived within the Gaussian approximation. Let us start with a brief review of the procedure used in Ref. 1 and a similar study reported in Ref. 3. In order to separate the relaxation due to direct transitions between the energy levels of the qubit, characterized by the time T1, the