Coherent Manipulation of Electronic States in a Double Quantum Dot

We investigate coherent time evolution of charge states (pseudospin qubit) in a semiconductor double quantum dot. This fully tunable qubit is manipulated with a high-speed voltage pulse that controls the energy and decoherence of the system. Coherent oscillations of the qubit are observed for several combinations of many-body ground and excited states of the quantum dots. Possible decoherence mechanisms in the present device are also discussed.

Figure 1

(a) Schematic measurement circuit combined with a scanning electron microscope image of the sample. Etching (upper and lower dark regions) and negatively biased gate electrodes ($G_L$, $G_l$, $G_C$, $G_r$, and $G_R$) define a double quantum dot (L and R) between the source (S) and drain (D). (b) Energy levels of the bonding ($E_b$) and antibonding ($E_a$) states, which are the eigenstates during the manipulation, and localized states ($E_L$ and $E_R$) during initialization. A typical condition of ${\epsilon }_1=0$, where $E_L$ and $E_R$ cross at $V_{sd}=0$, is shown. A typical pulsed voltage $V_{sd}(t)$ is shown at the bottom. (c)–(e) Energy diagrams of the DQD for ${\epsilon }_1=0$ during (c) initialization, (d) coherent oscillation, and (e) measurement process.

Figure 2

(a) Current profile, $I$ vs $V_R$, at constant $V_{sd}=650\mu \mathrm{V}$. Two resonant tunneling peaks, $\alpha$ and $\beta$, out of about six peaks in the transport window, are shown. The ground state resonant peak (not shown) is located at about 0.5 mV to the right of peak $\alpha$. Lorentzian fitting (dashed lines) to peaks $\alpha$ and $\beta$ gives approximate parameters $\hslash {\Gamma }_L\sim \hslash {\Gamma }_R\sim 30\mu \mathrm{e}\mathrm{V}$. (b) Color plot of $n_p$ as a function of $V_R$ and $t_p$. The horizontal axis is also shown in terms of ${\epsilon }_{0,i}$ and ${\epsilon }_{1,i}$ for resonance $i$ ($\alpha$ or $\beta$). (c) $n_p(t_p)$ at ${\epsilon }_1=0$ [long-dashed lines in (b)] for the resonance $\alpha$ (solid circles) and $\beta$ (open circles). Lines are fitted to the data. (d) The coupling energy, $\Delta$, determined from the oscillation frequency, when the gate voltage on $G_C$ is changed. The line is a guide for the eye.

Figure 3

Decoherence rate, $T_2^{-1}$, of the qubit. (a) The energy offset (${\epsilon }_1$) dependence. The dash-dotted line shows the decoherence rate, ${\Gamma }_{\epsilon }$, due to the fluctuation $\tilde{\epsilon }=1.6\mu \mathrm{e}\mathrm{V}$. (b) The coupling energy ($\Delta$) dependence. (c) The lattice temperature ($T_{\mathrm{l}\mathrm{a}\mathrm{t}}$) dependence. The solid (open) circles were measured with $\hslash {\Gamma }_L\sim \hslash {\Gamma }_R\sim 30\mu \mathrm{e}\mathrm{V}$ in sample I ($\hslash {\Gamma }_L\sim \hslash {\Gamma }_R\sim 13\mu \mathrm{e}\mathrm{V}$ in sample II). The decoherence rates calculated from cotunneling (${\Gamma }_{\mathrm{c}\mathrm{o}\mathrm{t}}$) and spin-boson model (${\Gamma }_{sb}$) are shown by solid and dashed lines, respectively.