Silicon is more than the dominant material in the conventional microelectronics industry: it also has potential as a host material for emerging quantum information technologies. Standard fabrication techniques already allow the isolation of single electron spins in silicon transistor-like devices. Although this is also possible in other materials, silicon-based systems have the advantage of interacting more weakly with nuclear spins. Reducing such interactions is important for the control of spin quantum bits because nuclear fluctuations limit quantum phase coherence, as seen in recent experiments in GaAs-based quantum dots1, 2. Advances in reducing nuclear decoherence effects by means of complex control3, 4, 5 still result in coherence times much shorter than those seen in experiments on large ensembles of impurity-bound electrons in bulk silicon crystals6, 7. Here we report coherent control of electron spins in two coupled quantum dots in an undoped Si/SiGe heterostructure and show that this system has a nuclei-induced dephasing time of 360 nanoseconds, which is an increase by nearly two orders of magnitude over similar measurements in GaAs-based quantum dots. The degree of phase coherence observed, combined with fast, gated electrical initialization, read-out and control, should motivate future development of silicon-based quantum information processors.
Figures at a glance
Figure 1: Device design. 
a, Device cross-section showing undoped heterostructure, dielectric and gate stack. b, Scanning electron micrograph of actual device before dielectric isolation and field gate deposition. Electrostatic gates are labelled L (left), T, R (right), PL, M, PR and Q; gates L and R are used for fast pulsing. The straight arrows show current paths for transport experiments (Supplementary Information), whereas the curved arrow shows the path of current through the QPC. A numerical simulation of the electron density for the two-electron (1,1) state is superimposed on the micrograph.
Figure 2: Spin blockade in the double quantum dot. 
a, Subregion of the charge stability diagram, showing the differential transconductance (black and white lines) of the charge-sensing QPC as a function of gate voltages. The trapezoidal spin blockade signature is seen with cyclic pulsing through the sequence (0,1)
(1,1) (0,2) (orange arrows). Being a differential measurement, the technique is sensitive only to changes in the average double-dot charge configuration, which is why only the edges of the trapezoidal blockade region are visible. The different colours indicate different responses of the QPC to electron movements on and between the dots. In particular, the current through the QPC decreases when electrons are added to either dot (white lines) but it increases when an electron transfers from the right dot to the left dot (black lines) (Supplementary Information). The voltage on gate Q (VQ) was swept with that on gate R (VR) to compensate for the capacitive coupling between gate R and the QPC and hence maintain constant sensitivity throughout the scan. b, Energy diagram of the (0,2)–(1,1) anticrossing, showing energies of the qubit states (1,1)S and (1,1)T0 and the Zeeman split (1,1)T± states as functions of detuning, ε. The exchange-energy splitting between qubit states, J(ε), the Zeeman splitting between triplet states, EZ, and the tunnel coupling, tc, are shown. c, Spin funnel obtained by measuring the degeneracy of (1,1)S and (1,1)T− as a function of ε and B. The width of the spin funnel implies a tunnel coupling, tc, of approximately 3 μeV. The functional form of J(ε) extracted from the funnel data is shown in Fig. 5.
Figure 3: Rabi oscillation pulse sequence and data. 
a, b, Essential elements of the pulse sequence used to obtain Rabi oscillations: VL and VR superimposed on the charge stability diagram (a); and represented as functions of time (b). The (0,2)S ground state is first prepared at point F with an exchange of an electron with the bath of the right-hand dot, if necessary. We then pulse to an intermediate point, P, before the subsequent adiabatic transition into the low-J ground state at point S, deep into (1,1). An exchange pulse and state rotation is then applied at E and followed by a return to S. The adiabatic transfer is then reversed and the dots are biased to point M for measurement, which generally consists of >90% of the pulse cycle. c, Rabi oscillations of the singlet probability, Ps, as a function of ε and exchange-pulse duration. d, Bloch sphere representations of state evolution for J > σHF (top) and J < σHF (bottom). Several instances of initial hyperfine ground states are shown as black dots (all with ΔHF > 0, for clarity), with corresponding rotation axes and trajectories. The data in c correspond to the average probability of returning to the initial prepared low-J ground state.
Figure 4: T2* pulse sequence and data. 
a, b, Essential elements of T2* pulse sequence. Analogous with the Rabi oscillation pulse sequence (Fig. 3a, b), we initialize in the (0,2)S ground state at F and then pulse to intermediate point P. We then non-adiabatically pulse deeply into (1,1) to point S (this is the separation pulse) for a variable amount of time for singlet dephasing, and then return non-adiabatically to point M for measurement. c, Evolution of (1,1)S as indicated by Ps, as a function of separation time for several different separation-pulse detunings (residual J). Coloured circles show measured data; the least-squares fit (black lines) and 1-s.d. confidence intervals (coloured bands) for a hyperfine-averaged model23, 26 are superimposed. The values of J/σHF resulting from this fit are shown in the key. d, Bloch sphere representations of an ensemble of trajectories, with J/σHF values as indicated by colour in c. The ensemble of rotation axes is also shown in each case. The data in c correspond to the average projection of trajectories onto the z axis.
Figure 5: Effective exchange energy versus detuning. 
J(ε) extracted from the spin funnel data (Fig. 2c), Rabi oscillation data (Fig. 3c) and T2* data (Fig. 4c). J ranges from 0.6 to 700 neV with excellent agreement where these data sets overlap (Supplementary Information). Error bars on the T2* data (blue) and the confidence interval for the Rabi data (green) are 1-s.d. fit-parameter uncertainties; spin funnel symbol sizes correspond to Gaussian-fit transition widths. The grey band denotes the estimated σHF value from the T2* data.
