Decoherence of a quantum two-level system by spectral diffusion

Abstract

We study the dephasing of an individual high-frequency tunneling two-level system (TLS) due to its interaction with an ensemble of low-frequency thermal TLSs which are described by the standard tunneling model (STM). We show that the dephasing by the bath of TLSs explains both the dependence of the Ramsey dephasing rate on an externally applied strain as well as its order of magnitude, as observed in a recent experiment [J. Lisenfeld et al.]. However, the theory based on the STM predicts the Hahn-echo protocol to be much more efficient, yielding too low echo dephasing rates, as compared to the experiment. Also the strain dependence of the echo dephasing rate predicted by the STM does not agree with the measured quadratic dependence, which would fit to a high-frequency white noise environment. We suggest that few fast TLSs which are coupled much more strongly to the strain fields than the usual TLSs of the STM give rise to such a white noise. This explains the magnitude and strong fluctuations of the echo dephasing rate observed in the experiment.

Transport signatures of a Majorana qubit and read-out-induced dephasing

“…We see a rapid initial decay with rate given by Γ −1 , followed by a slow decay with rate λ 0 2 /Γ, which is visible only in the case when λ 0 = Γ. This rate is well known from situations where a qubit is subject to telegraph noise [27][28][29][30][31] in the considered limit, where the amplitude of the noise (i.e. the energy shift of the qubit due to the noise) is low compared to rate of switching.…”

Rabi noise spectroscopy of individual two-level tunneling defects

“…Using standard estimations within the STM, one expects the relaxation rates Γ 1 of thermal TLSs (at T = 35 mK) to be smaller than 10 ms −1 . 17,19 Consequently, these fluctuators are in the regime Γ 1 Ω R , Γ Echo and thus give rise to quasistatic noise, for whichX is constant during each run of the experiment but fluctuates between different runs. These fluctuators will not contribute to Γ ν and Γ Echo .…”

“…As a result, close to the symmetry point ε = 0 (thus cos θ 1) one may assume X cos θ Ω R . We therefore expand In contrast to the Ramsey dephasing, 17,19 which is caused by individual thermal TLSs, the last term of Eq. (8) shows that the second-order contribution to the Rabi dephasing is due to pairs of thermal TLSs.…”

“…However, since a product of two RTPs with flipping rates γ 1 and γ 2 is also a RTP with flipping rate γ 1 + γ 2 , the second-order contribution to the Rabi dephasing is essentially similar to the Ramsey dephasing. 17,19 The decay law due to this low-frequency noise is…”

“…We employ a theoretical model based on interacting TLSs and find agreement with the experimentally observed magnitude of the Rabi dephasing rate and its dependence on the applied strain and on the Rabi frequency. In conjunction with measurements of energy relaxation, Ramsey and echo dephasing, 17,19 Rabi noise spectroscopy provides information about the spectrum of the environment to which TLSs couple, within three different spectral ranges. This allows one to distinguish between contributions from distinct environmental degrees of freedom.…”