Fig. 4
Zeeman energy differences and simulated S-T 0 oscillation contrasts. a The Zeeman energy in each dot is determined using EDSR measurements for a range of magnetic field strengths28, 34 and is fitted to E z = |g 1 μ B B + g 3 μ B B 3|, resulting in \(g_1^{{\rm{dot1}}} = - 0.4332 \pm 0.0005\), \(g_3^{{\rm{dot1}}} = \left( {0.47 \pm 0.03} \right){10^{ - 3}}\)/T2, \(g_1^{{\rm{dot2}}} = - 0.4353 \pm 0.0004\), \(g_3^{{\rm{dot2}}} = \left( {0.46 \pm 0.04} \right){10^{ - 3}}\)/T2, \(g_1^{{\rm{dot3}}} = - 0.4361 \pm 0.0006\), \(g_3^{{\rm{dot3}}} = \left( {0.47 \pm 0.04} \right){10^{ - 3}}\)/T2, \(g_1^{{\rm{dot4}}} = - 0.4372 \pm 0.0004\), \(g_3^{{\rm{dot4}}} = \left( {0.47 \pm 0.03} \right){10^{ - 3}}\)/T2. The solid data points represent the differences in Zeeman energy between dot n (n = 2,3,4) and dot 1 as a function of magnetic field, extracted from the EDSR measurements (error bars account for the expected fluctuations of ± 15 MHz from the quasi-static nuclear field and ± 5 MHz from the frequency resolution of the measurement, for each of the two resonance measurements used in the frequency difference calculation). Solid curves represent the difference between the fit of dot n and dot 1. Open circles show the Zeeman energy differences extracted from Figs. 3a–c (error bars indicate the fitting uncertainty). b The contrast of the simulated coherent oscillation when pulsing from point I to point A in Fig. 1b. The simulation assumes a linear ramp from start to end over 2.50 ns. c Similar to b but pulsing to point B and varying the tunnel coupling between dots 2 and 3. d Similar to b but pulsing to point C and varying the tunnel coupling between dots 3 and 4. The tunnel couplings were set to t 12 = 1.2, t 23 = 2.6, and t 34 = 4.3 GHz if not varied. These values correspond to the peak positions in the tunnel coupling dependencies. Note that the maximum in d is lower and occurs for a higher tunnel coupling than that in c because the ramp rate is higher for d (same ramp duration but higher pulse amplitude)
