Fig. 4 | Nature Communications

Fig. 4

From: Two-electron spin correlations in precision placed donors in silicon

Fig. 4

Theoretical predictions for the observation of coherent exchange oscillations. a The value of exchange energy, J, as a function of tunnel coupling, tc and detuning, \(\epsilon\). The boundary separating the two-electron product states with singlet-triplet states occurs where the difference in magnetic field between the two qubits, ΔBz is equal to the exchange energy. For donor-based systems ΔBz is dominated by the donor hyperfine strength, and is equal to A for a 1P−1P system (solid green line), and can take the two values A/2 or 3A/2 for a 2P−1P system (dashed and dotted green lines respectively) dependent on the nuclear spin orientation (examples shown in inset). We assume the bulk 1P value for the hyperfine, A = 117.53 MHz. The dashed blue line indicates the values of J accessible for the current device with tc ~ 200 MHz. b Theoretical prediction of coherent exchange oscillations for a 2P−1P device in natural silicon with tunnel coupling tc = 2.5 GHz. The two-electron state is initialised as \(\left| { \uparrow \downarrow } \right\rangle _{}^{}\) at a point where the exchange energy is negligible, and subsequently a non-adiabatic detuning pulse is applied to \(\epsilon\) = −25 GHz (circle marker in a). We have assumed voltage noise equivalent to 850 MHz along the detuning axis, \(\epsilon\) (obtained from measurements) as well as a single electron \(T_2^ \ast = {55\,{\mathrm {ns}}}\) measured in previous works32. From this result an oscillation frequency ν and dephasing time τd are extracted. c The product of oscillation frequency, ν and dephasing time, τd as a function of tunnel coupling and detuning. The green dashed line represents the boundary between product and singlet-triplet eigenstates of the two-electron system. The Bloch sphere cross sections indicate the relative magnitudes of ΔBz (purple) and J (blue) in different regions. d Theoretical prediction of ντd along the line ΔBz = J as a function of tunnel coupling for a 2P−1P double quantum dot. Solid (dashed) line shows results including (excluding) the 29Si Overhauser field

Back to article page