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arXiv:cond-mat/0404641

Dephasing due to nonstationary 1/f noise

Josef Schriefl, Maxime Clusel, David Carpentier, Pascal Degiovanni, Yuriy Makhlin

Published Jan 1, 2004• 0 citations
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Abstract

Motivated by recent experiments with Josephson qubits we propose a new phenomenological model for 1/f noise due to collective excitations of interacting defects in the qubit's environment. At very low temperatures the effective dynamics of these collective modes are very slow leading to pronounced non-Gaussian features and nonstationarity of the noise. We analyze the influence of this noise on the dynamics of a qubit in various regimes and at different operation points. Remarkable predictions are absolute time dependences of a critical coupling and of dephasing in the strong coupling regime.

DOI
10.48550/arxiv.cond-mat/0404641

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The efficiency of the future devices for quantum information processing will be limited mostly by the finite decoherence rates of the qubits. Recently, substantial progress was achieved in enhancing the time within which a solid-state qubit demonstrates coherent dynamics. This progress is based mostly on a successful isolation of the qubits from external decoherence sources. Under these conditions, the material-inherent sources of noise start to play a crucial role. In most cases, the noise that the quantum device demonstrates has a 1/ f spectrum. This suggests that the environment that destroys the phase coherence of the qubit can be thought of as a system of two-state fluctuators, which experience random hops between their states. In this short review, the current state of the theory of the decoherence due to the qubit interaction with the fluctuators is discussed. The effect of such an environment on two different protocols of the qubit manipulations, free induction and echo signal, is described. It turns out that in many important cases the noise produced by the fluctuators is non-Gaussian. Consequently, the results of the interaction of the qubit with the fluctuators are not determined by the pair correlation function alone. We describe the effect of the fluctuators using the so-called spin-fluctuator model. Being quite realistic, this model allows one to exactly evaluate the qubit dynamics in the presence of one fluctuator. This solution is found, and its features, including non-Gaussian effects, are analyzed in detail. We extend this consideration to systems of large numbers of fluctuators, which interact with the qubit and lead to the 1/ f noise. We discuss existing experiments on the Josephson qubit manipulation and try to identify non-Gaussian behavior.
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We consider a phenomenological model for a $1∕{f}^{\ensuremath{\mu}}$ classical intermittent noise and study its effects on the dephasing of a two-level system. Within this model, the evolution of the relative phase between the $\ensuremath{\mid}\ifmmode\pm\else\textpm\fi{}⟩$ states is described as a continuous time random walk (CTRW). Using renewal theory, we find exact expressions for the dephasing factor and identify the physically relevant various regimes in terms of the coupling to the noise. In particular, we point out the consequences of the nonstationarity and pronounced non-Gaussian features of this noise, including some anomalous and aging dephasing scenarios.