Optical Control in Coupled Two-Electron Quantum Dots

The dynamics of two electrons in a 2-dimensional quantum dot molecule in the presence of a time-dependent electromagnetic field is calculated from first principles. We show that carefully selected microwave pulses can exclusively populate a single state of the first excitation band and that the transition time can be further decreased by optimal pulse control. Finally we demonstrate that an oscillating charge localized state may be created by multiple transitions using a sequence of pulses.

Figure 1

The figure shows the 10 lowest singlet energy levels of the field free Hamiltonian of Eq. (1) with $d=130\mathrm{nm}$, $V_{\mathrm{ext}}=0$, and $\hslash \omega =1\mathrm{meV}$. The $\pm$ indicates the $x$ parity of the highlighted states.

Figure 2

One-electron densities (left column) and conditional densities (right column). The conditional densities are evaluated at one maximum of the wave function, for each electron (solid and dashed lines). Upper panel: ground state, middle panel: 2nd excited state, and lower panel: 6th excited state. The right column shows that the two upper states may be regarded as “covalent” states, whereas the lower state is an “ionic” state with both electrons in the same dot. The double dot potential is also shown. The interdot distance is $d=130\mathrm{nm}$. Both axes in the left column range from $-165$ to 165 nm.

Figure 3

Upper panel: Controlled transition from the ground state to the first excited state, $|g,+⟩\to |e,-⟩$ with ${\omega }_I=1.5\mathrm{THz}$ and $I_I=0.39\mathrm{W}/{\mathrm{cm}}^2$ (solid line). The dashed curve shows the transition using an optimized pulse. Lower panel: Time development of a few selected states for the same pulse as above with intensity $I_I=3.86\mathrm{W}/{\mathrm{cm}}^2$. The population shown is for the ground state (thick dashed line), second excited state (thick solid line), 7th excited state (dash-dotted line), 11th excited state (thin solid line), and 24th excited state (dotted line).

Figure 4

Population of states during the sequence of pulses. The duration of the individual pulses is indicated by dashed vertical lines. The thin dashed line is the ground state population. The thick dotted line is the population of the excited state $|e,-⟩$. The two lines that exhibit beats during pulse III are the population of the states $|\mathrm{ion},+⟩$ (upper) and $|\mathrm{ion},-⟩$ (lower). Upper panel: $\hslash \omega =1\mathrm{meV}$ and $d=130\mathrm{nm}$. The inset shows the last transition modeled by a four-level system. Middle panel: $\hslash \omega =3\mathrm{meV}$ and $d=60\mathrm{nm}$. Lower panel: Single-particle probability density for the field free propagation of the charge localized state at $t=0$, $t=1/4T_{\mathrm{CLS}}$ and $t=1/2T_{\mathrm{CLS}}$. The period is $T_{\mathrm{CLS}}=180\mathrm{ps}$.