Fig. 3
From: Coherent transfer of electron spin correlations assisted by dephasing noise
Coherent transfer of spin entanglement. a Illustration of the entanglement transfer process. Local spin entanglement is prepared in QD3 and then split to the nearest neighbors (QD2, QD3), followed by the noise-assisted transfer to distant sites (QD1, QD3). b Coherent evolutions of the distant entanglement (taken at ε/h = −44 GHz, red circles) and the nearest-neighbor entanglement (ε/h = −7 GHz, blue circles offset for clarity). The simulation data are scaled to take into account the readout error in the data (Methods section). The singlet-return probability PS inferred from the single-shot spin blockade measurement is plotted as a function of tevolve. The data points are obtained by performing a Gaussian convolution filter of the width σ ε = 0.9 GHz for the detuning. Solid lines show the numerical calculations of the coherent evolutions at ε/h = −44 GHz (red and gray) and ε/h = −7 GHz (blue) with the dephasing rates \(\gamma _{t_{\mathrm{L}}} = 1.7\,{\mathrm{GHz}}\), \(\gamma _{t_{\mathrm{R}}} = 0.12\,{\mathrm{GHz}}\) and \(\gamma _{\varepsilon _{{\mathrm{L,R}}}}/\gamma _{t_{{\mathrm{L,R}}}} = 100\) (red and blue) and with the smaller rates of \(\gamma _{t_{\mathrm{L}}} = 17\,{\mathrm{MHz}}\) and \(\gamma _{t_{\mathrm{R}}} = 1.2\,{\kern 1pt} {\mathrm{MHz}}\) (gray). The simulation results are reproduced from Fig. 4c by choosing corresponding detuning values marked by stars. The envelopes of the oscillations correspond to a Gaussian decay with \(T_2^ \ast \approx 60{\kern 1pt} {\mathrm{ns}}\) for both cases due to the Overhauser field fluctuation5 during the ensemble averaging time of 22.7 s. This phase averaging effect is independent of the Markovian dephasing noise which is dominant only around ε = εL,R as discussed later
