Nonadiabatic quantum control of a semiconductor charge qubit

We demonstrate multipulse quantum control of a single electron charge qubit. The qubit is manipulated by applying nonadiabatic voltage pulses to a surface depletion gate and readout is achieved using a quantum point-contact charge sensor. We observe Ramsey fringes in the excited-state occupation in response to a $\pi /2$-$\pi /2$ pulse sequence and extract $T_2^{*}\sim 60$ ps away from the charge degeneracy point. Simulations suggest these results may be extended to implement a charge echo by reducing the interdot tunnel coupling and pulse rise time, thereby increasing the nonadiabaticity of the pulses.

Figure 1

(a) Scanning electron microscope image of a sample similar to the one measured. The triple quantum dot is configured as a double dot, with the third dot operated as a charge sensor. Ohmic contacts to the 2DEG are marked by black squares. Voltage pulses are applied to the left gate (labeled L). (b) Charge sensor conductance $g_Q$ measured near the (0,1)-(1,0) charge transition with nonadiabatic pulses applied. The dashed line shows a typical range of gate voltages where qubit state readout is performed. (c) Qubit energy-level diagram. A typical voltage pulse is shown in the lower panel. (d) Coherent oscillations are obtained by varying the pulse width $t_p$.

Figure 2

(a) Ramsey fringe pulse sequence depicted in the Bloch sphere representation. The qubit is initialized in $|R\rangle$. A ${\sigma }_x=\pi /2$ pulse rotates the Bloch vector to the equator. The qubit then freely evolves for a variable time $\tau$, resulting in a ${\sigma }_z$ rotation on the Bloch sphere. The final state is determined using charge sensing after a second ${\sigma }_x=\pi /2$ pulse is applied. (b) A typical voltage pulse profile with $t_{\pi /2}=130$ ps. (c) QPC conductance measured as a function of delay $\tau$ for a pulse amplitude $V_p=900$ mV. The two pulses partially overlap for $\left|\tau \right|<140$ ps, resulting in Larmor precession similar the data in Fig. 1d. Ramsey fringes are observed for longer delay times.

Figure 3

(a) Ramsey fringes with a fit to Eq. (2). The value for $T_2^{*}$ extracted from the fit is $60\pm 10$ ps. (b) Ramsey frequency as a function of $V_L$ extracted from experimental data (in red). The black line shows the expected frequency based on spectroscopy of the energy-level diagram. (c) Excited-state occupation $P_L$ as a function of $V_L$ and $\tau$. The dashed line shows the location of the cut in (a). (d) Numerical simulation of the excited-state occupation generated using pulse profiles acquired at the output of the pulse generator, plotted on the same color scale as the experimental data in (c).

Figure 4

(a) Evolution of the charge qubit during an ideal charge-echo pulse sequence. (b) A typical pulse sequence, as acquired at the output of the pulse generator. (c) Excited-state probability $P_L$ as a function of $V_L$ and the displacement $\delta t$. (d) Expanded plots of $P_L$ as a function of $V_L$ and $\delta t$ near $\delta t=0$ for (i) experimental data (c), (ii) simulation using experimental pulses, (iii) simulation with $\Delta /h=0.5$ GHz and using ideal Gaussian pulses (see text) with $V_p=300$ mV and a rise time of 60 ps, and (iv) simulation with $\Delta /h=0.5$ GHz using experimental pulses with $V_p=300$ mV.