Fig. 5
From: Coherent transfer of electron spin correlations assisted by dephasing noise
Markovian dephasing measurement of the three-spin system. a Exchange oscillation (SWAP) between \(\left| {\sigma _1 \uparrow _2 \downarrow _3} \right\rangle\) and \(\left| {\sigma _1 \downarrow _2 \uparrow _3} \right\rangle\) driven by a brief excursion to ε/h = 25 GHz for the duration of t, following the adiabatic loading of \(\left| {\sigma _1 \downarrow _2 \uparrow _3} \right\rangle\) (Methods section). Red and blue lines are the fits to the decaying oscillations \(A{\rm exp}\left[ - \left( {t/T_2^{( \ast )}} \right)^a\right]{\rm cos}\left( {Et/\hbar + \phi } \right) + B\), with exponential (a = 1 with the dephasing time T2) and Gaussian (a = 2 with the emsemble dephasing time T2*) envelopes, respectively. b The dephasing rate \(T_2^{ - 1}\) (red circles) and the oscillation frequency E kl /h (blue circles) extracted from the fits as in a with the exponential envelope at various ε with the error bars representing the standard errors of the fitting. Blue lines represent energy gaps for E21 and E32 calculated with the same parameters as those used in Figs. 2 and 4 except for ΔB12/h = 90.5 MHz and ΔB23/h = 26.7 MHz determined by the fitting. Those values differ from the ones derived in Fig. 4 due to the slow Overhauser field fluctuation. Red lines are the dephasing rates Γ12 and Γ23 arising from the charge noise modeled by Eq. 1 for different magnitudes of \(\gamma _{\varepsilon _{{\mathrm{L,R}}}}/\gamma _{t_{{\mathrm{L,R}}}}\). The values of \(\gamma _{t_{\mathrm{L}}}\) and \(\gamma _{t_{\mathrm{R}}}\) used in Figs. 3b and 4c are derived from the fitting by choosing \(\gamma _{\varepsilon _{{\mathrm{L,R}}}}/\gamma _{t_{{\mathrm{L,R}}}} = 100\). The data points with red empty circles deviate from the model because the fluctuation of ΔB ij also contributes to the Gaussian decay and a fitting with an exponential envelope is unreliable in the corresponding detuning range
