Optimal laser control of double quantum dots

Coherent single-electron control in a realistic semiconductor double quantum dot is studied theoretically. Using optimal-control theory, we show that the energy spectrum of a two-dimensional double quantum dot has a fully controllable transition line. We find that optimized picosecond laser pulses generate population transfer at significantly higher fidelities $(>0.99)$ than conventional sinusoidal pulses. Finally, we design a robust and fast charge switch driven by optimal pulses that are within reach of terahertz laser technology.

Figure 1

(Color online) Left panel: lowest eigenenergies of a double quantum dot with ${\omega }_0=0.5$ as a function of the interdot distance. Black, red (thick), and blue (thin) curves mark the ground state, controllable states, and uncontrollable states, respectively. Right panel: densities of six lowest eigenstates at $d=5$. The dashed lines mark the nodes of the wave functions.

Figure 2

(Color online) Maximum occupation (logarithmic scale) of the target state as a function of the interdot distance $d$ in transitions $\mid 00⟩\to \mid 10⟩$ with pulse length $T=50$ (circles) and $\mid 00⟩\to \mid 20⟩$ with $T=100$ (squares). The lines are guides for the eyes. The dashed line denotes the maximum target-state occupation of 0.6 for a single harmonic oscillator. The jump marked by an arrow is due to a resonance effect (see text).

Figure 3

(Color online) Upper panel: optimized pulses ($x$ components) for transitions (a) $\mid 00⟩\to \mid 10⟩$ and (b) $\mid 00⟩\to \mid 20⟩$. The interdot distances are fixed to $d=3$ and 5 and the pulse lengths to $T=50$ and 100, respectively. Lower panel: occupations of states involved in the transitions.

Figure 4

(a) Spectrum of the optimized pulse (inset) for the electron transport process $\mid L⟩\to \mid R⟩$ in a fixed time $T=100$. The pulse has a rectangular envelope $A\left(t\right)=1$, and the penalty factor is $\alpha =1$. (b) Occupations of states $\mid R⟩$ and $\mid L⟩$ (solid lines) and the integrated densities ${\rho }_R$ and ${\rho }_L$ (dashed lines) in the right and left dots during the transport. (c)–(h) Snapshots of the total electron density ${\rho }_R+{\rho }_L$. The double quantum dot has $d=6$, ${\omega }_0=0.5$, and well-depth asymmetry of $V_0=0.2$.