Quantum Coherence in a One-Electron Semiconductor Charge Qubit

We study quantum coherence in a semiconductor charge qubit formed from a GaAs double quantum dot containing a single electron. Voltage pulses are applied to depletion gates to drive qubit rotations and noninvasive state readout is achieved using a quantum point contact charge detector. We measure a maximum coherence time of $\sim 7\mathrm{ns}$ at the charge degeneracy point, where the qubit level splitting is first-order insensitive to gate voltage fluctuations. We compare measurements of the coherence time as a function of detuning with numerical simulations and predictions from a $1/f$ noise model.

Figure 1

(a) Scanning electron micrograph of a device similar to the one measured. (b) Charge sensor conductance, $g_Q$, measured near the $(1,0)-(0,1)$ charge transition. (c) Peak height versus linewidth of the microwave-induced resonances for different applied microwave powers. The solid curve is a fit to theory (see text). Inset: Left dot occupation, $P_{(1,0)}$, as a function of detuning, $ϵ$, for a microwave peak at two different powers. The solid lines show Gaussian fits to the data. (d) Microwave spectroscopy data acquired for three different values of $V_M$.

Figure 2

(a) Charge qubit energy level diagram. The arrows indicate the pulse sequence and two different reset mechanisms. (b) Bloch sphere representation of charge qubit evolution at zero detuning. (c) Charge stability diagram measured with a $t_p=150\mathrm{ps}$ pulse applied. Overlaid is a typical 150 ps pulse, as produced by the pulse generator. (d) Differentiated version of the data in (c).

Figure 3

(a) Coherent charge oscillations as a function of pulse width and detuning. (b) Simulated coherent oscillations. (c) Qubit evolution acquired at ${ϵ}_p=0$ for two values of the tunnel coupling.

Figure 4

(a) Data from Fig. 3a corrected to take into account the reduced pulse amplitude at short pulse widths. (b) Fits to the coherent oscillations at three different detunings as indicated in (a). (c) Coherence rates extracted from the fits as a function of detuning. The dashed line shows the expected behavior based on a simple low-frequency noise model with ${\sigma }_{ϵ}=3.9\mu \mathrm{eV}$. The solid line shows the coherence rates extracted from simulations with ${\sigma }_{ϵ}=5\mu \mathrm{eV}$.