Correlated Coherent Oscillations in Coupled Semiconductor Charge Qubits

We study coherent dynamics of two spatially separated electrons in a coupled semiconductor double quantum dot (DQD). Coherent oscillations in one DQD are strongly influenced by electronic states of the other DQD, or the two electrons simultaneously tunnel in a correlated manner. The observed coherent oscillations are interpreted as various two-qubit operations. The results encourage searching quantum entanglement in electronic devices.

Figure 1

(a) Colored SEM image of the control device (blue and black, respectively, for unetched and etched surface, and gold for metal gates). The circles represent quantum dots in DQD1 and DQD2. All measurements were performed at electron temperature of 100 mK at magnetic field of 0.6 T. The energy offsets, ${\epsilon }_1$ and ${\epsilon }_2$, and tunneling coupling, ${\Delta }_1$ and ${\Delta }_2$, were independently controlled by changing some gate voltages simultaneously to compensate for electrostatic crosstalk. Tunneling rates are ${\Gamma }_{L1}\sim {\Gamma }_{R1}\sim {\Gamma }_{L2}\sim {\Gamma }_{R2}\sim 1\mathrm{GHz}$ for the left (L) and right (R) barrier of the first (1) and second (2) DQD. (b) and (c) Charge diagram of the ground state at ${\Delta }_1={\Delta }_2\sim 0$ in (b) and of the first excited state at ${\Delta }_1=13\mu \mathrm{eV}$, ${\Delta }_2=25\mu \mathrm{eV}$, and $J=25\mu \mathrm{eV}$ in (c). Colors represent the charge state, LL (cyan), LR (magenta), RL (yellow), and RR (white). The resonant conditions are indicated by solid and dashed lines. Energy diagrams at some points (▹◃$\ominus \oplus$) for CROT, SWAP, and FLIP operations are shown in the insets. (d) Electrochemical potential of DQD1 and DQD2 in the steady state for initialization at large bias (Ini1 and Ini2), in the coherent evolution at zero bias (Evo1 and Evo2), and in the measurement at large bias (Meas1 and Meas2). A schematic of the voltage pulse is shown at the top.

Figure 2

(a) and (b) First-order coherent oscillations (CROT operations) for the initial state $|LR⟩$ in (a) and for $|LL⟩$ in (b). (c) to (e) $N_{P1}$ in the ${\epsilon }_1\mathrm{\text{−}}{\epsilon }_2$ plane obtained at a fixed $t_p=0.25\mathrm{ns}$ ($\pi$ pulse for the CROT operations). The energy offsets in the initialization period (${\epsilon }_1^{\prime }$ and ${\epsilon }_2^{\prime }$) are shown in the right and top scales [${\epsilon }_1^{\prime }\simeq {\epsilon }_1-50\mu \mathrm{eV}$ and ${\epsilon }_2^{\prime }\simeq {\epsilon }_2-20\mu \mathrm{eV}$]. (f) Correlated coherent oscillations at ${\epsilon }_1\sim 25\mu \mathrm{eV}$ along the solid line in (e). (g) Density matrix simulation of (f). (h) Typical $N_{p1}(t_p)$ traces; the first-order [${\epsilon }_1=-J/2$ of (b)] and correlated coherent oscillations (${\epsilon }_2\sim 10\mu \mathrm{eV}$).

Figure 3

Correlated cotunneling current in simultaneous measurement of $I_1$ in (a) and $I_2$ in (b) in the ${\epsilon }_1^{\prime }\mathrm{\text{−}}{\epsilon }_2^{\prime }$ plane measured at $V_{D1}=700\mu \mathrm{eV}$ and $V_{D2}=10\mu \mathrm{eV}$. Solid and dotted lines are current traces at ${\epsilon }_2^{\prime }\sim 50\mu \mathrm{eV}$ and $-10\mu \mathrm{eV}$, respectively. Second-order tunneling peaks $\alpha$, $\beta$, and ${\beta }^{\prime }$ appear at the same marks in Fig. 2e.