All-electrical coherent control of the exciton states in a single quantum dot

We demonstrate high-fidelity reversible transfer of quantum information from the polarization of photons into the spin state of an electron-hole pair in a semiconductor quantum dot. Moreover, spins are electrically manipulated on a subnanosecond time scale, allowing us to coherently control their evolution. By varying the area of the electrical pulse, we demonstrate phase-shift and spin-flip gate operations with near-unity fidelities. Our system constitutes a controllable quantum interface between flying and stationary qubits, an enabling technology for quantum logic in the solid state.

Figure 1

(Color online) (a) Schematic energy diagram of the QD used in our experiment where the polarization of the laser is transferred into the exciton’s spin state through quasiresonant excitation. [(b) and (c)] Evolution of $\left|s\right|$ and orientation of the eigenstates relative to the lab-frame as a function of vertical electric field. Spectral and temporal measurements of $\left|s\right|$ are in good agreement. (d) High-visibility coherent oscillations of the spin state for three different values of $\left|s\right|$. The exciton was initialized in a maximum superposition of eigenstates and emission was time-resolved along the same orientation.

Figure 2

(Color online) (a) Operating principle of our solid-state photonic interface. An optical qubit $|{\Psi }_{in}⟩$ is first encoded in the polarization of a photon. Quantum information is then coherently transferred from $|{\Psi }_{in}⟩$ into the spin state $|{\Psi }_X\left(t\right)⟩$ of the exciton which rotates around the equatorial plan of the Bloch sphere at an angular velocity $\left|s\right|/\hslash$. Finally, the electron-hole pair recombines and emits a photon of polarization $|{\Psi }_{out}⟩$ depending on the time spent in the solid state. (b) Complete characterization of the time evolution of $|{\Psi }_X\left(t\right)⟩$ prepared in the $|X_D⟩$ spin state by time-resolved measurements in linear, diagonal, and circular bases. Each signal has been normalized by the sum of the two measurements in the corresponding basis (vertical scale from 0 to 1). The symbols refer to measurements along different polarizations. (c) Fidelity $f_{in}={\left|⟨{\Psi }_{out}|{\Psi }_{in}⟩\right|}^2$ of the interface. The symbols refer to different input qubits.

Figure 3

(Color online) (a) The electrical gate modulates $\left|s\right|$ and induces a faster phase accumulation between the spin eigenstates. The gated time-evolution (bottom) is consequently dephased compared to the ungated operation (top). (b) Phase shift as a function of gate amplitude. (c) Normalized (color scale from 0 to 1) time-resolved data for an exciton initialized in a diagonal superposition $|X_D⟩$ and measurements in the diagonal basis. [(d) and (e)] Radiative emission from the QD initialized in $|X_D⟩$, respectively, without gate and with a $\pi$ phase-shift gate. (f) Fidelity of the $\pi$-shift gate operation as a function of time.

Figure 4

(Color online) (a) Operating principle of the spin-flip gate. The exciton is initialized at minimum splitting in its eigenstate $|X_D⟩$. Modulating the electric field changes the value of $\left|s\right|$ and rotates the eigenstates by $45°$ resulting in a superposition $|X_D⟩$. A $\pi$ phase shift is accumulated during the gate operation leading to a superposition $|X_A⟩$. Returning to the initial value of the electric field induces another $45°$ rotation of the eigenstates resulting in a spin flip. [(b) and (c)] Radiative emission from the QD, respectively, without gate and with the spin-flip gate. The trace with empty (plain) circles is obtained when exciting and measuring along the same (opposite) eigenstates. (d) Fidelity of the spin-flip gate as a function of time.