High-Finesse Optical Quantum Gates for Electron Spins in Artificial Molecules

A doped semiconductor double-quantum-dot molecule is proposed as a qubit realization. The quantum information is encoded in the electron spin, thus benefiting from the long relevant decoherence times; the enhanced flexibility of the molecular structure allows one to map the spin degrees of freedom onto the orbital ones and vice versa and opens the possibility for high-finesse (conditional and unconditional) quantum gates by means of stimulated Raman adiabatic passages.

Figure 1

Schematic representation of our proposed qubit implementation which consists of two vertically coupled quantum dots in the presence of an external electric field. (a) Level scheme as described in the text: single-electron states $|0⟩$ and $|1⟩$ (electron in large dot $L$ and $|S_x=\mp \frac{\mathrm{1}}{\mathrm{2}}⟩$, respectively) which are used to encode the quantum information; auxiliary state $|2⟩$ (electron in small dot $S$ and $|S_x=-\frac{\mathrm{1}}{\mathrm{2}}⟩$); charged-exciton state $|3⟩$ which allows optical coupling between all single-electron states through frequency-selective and linearly polarized laser pulses (Rabi energies ${\Omega }_{i,{\sigma }_i}$, light polarizations ${\sigma }_{0,2}=x$, and ${\sigma }_1=y$). (b) [(c)] Square modulus of the electron wave function along $z$ in the large dot $L$ [small dot $S$].

Figure 2

Implementation of the controlled-NOT gate for an initial state $|1{⟩}_c\otimes |0{⟩}_t$ [panel (a)]; (b) a first adiabatic passage sequence applied to the control qubit transfers the electron to the smaller dot $S_c$ and changes the electrostatic potential; (c) a NOT transformation is applied to the target qubit with the laser frequencies tuned to the modified transition energies; (d) a final STIRAP sequence brings back the control qubit to its initial state. The symbols below each dot molecule indicate the nature of information storage (spin or orbital) at different stages of the quantum gate.

Figure 3

Results of our calculations. (a) Spatial distributions along $z$ for the electron states 0, 1, 2 (lower plots) and for the exciton state $X^{-}$ (upper plot; light and dark gray correspond to electrons and holes, respectively). The lateral confinement of the carriers is produced by a parabolic potential, with $\hslash {\omega }_{e,h}=60$, 50 meV, while the applied electric field is $\mathbf{F}=-3\widehat{\mathbf{z}}+50(\widehat{\mathbf{x}}+\widehat{\mathbf{y}})\mathrm{k}\mathrm{V}/\mathrm{c}\mathrm{m}$. (b) Absorbtion spectra corresponding to the three possible initial states 0, 1 (lower spectrum) and 2 (upper spectrum), where the photon zero corresponds to the semiconductor band gap. The shaded regions indicate the energies of the pump and Stokes pulses. The Zeeman splitting of the 0 and 1 states, induced by the magnetic field, is neglected in the calculations. The physical parameters (GaAs) are the following: $m_{e,h}^{*}=0.067m_0$, $0.80m_0$, band offsets $V_0^{e,h}=400$, 215 meV, and dielectric constant $ϵ=12.9$.