Ultrafast sequential charge transfer in a double quantum dot

We use optimal control theory to construct external electric fields that coherently transfer the electronic charge in a double quantum-dot system. Without truncation of the eigenstates we operate on desired superpositions of the states in order to prepare the system to a localized state and to coherently transfer the charge from one well to another. Within a fixed time interval, the optimal processes are shown to occur through several excited states. The obtained yields are generally between 99% and 99.99% depending on the field constraints, and they are not dramatically affected by strict frequency filters which make the fields (e.g., laser pulses) closer to experimental realism. Finally we demonstrate that our scheme provides simple access to hundreds of sequential processes in charge localization while preserving the high fidelity.

Figure 1

(Color online) Model potential for the quantum dot (black solid line), the ground state (green line), the first excited state (black dashed-dotted line), and their superpositions corresponding to left (red dotted line) and right (blue dashed line) states.

Figure 2

(Color online) (a) Optimized field to prepare the system to the superposition $|L⟩$ (see text) from the ground state. (b) Occupations of the ground state $|0⟩$, first excited state $|1⟩$, and their superposition $|L⟩$.

Figure 3

(Color online) (a) Optimized fields without (thin blue line) and with spectral constraints (thick red line) for transition $|L⟩\to |R⟩$. [(b) and (c)] Occupations of the five lowest eigenstates during the process. (d) Occupations of the initial and target superposition states.

Figure 4

(Color online) (a) Spectrum of the optimized field for the process $|L⟩\to |R⟩$ without (blue thin line) and with a spectral constraint (red thick line) at ${\omega }_{\text{th}}=0.817$. (b) Occupation of target state as the function of the frequency threshold ${\omega }_{\text{th}}$ used as the filter. The steplike form of the curve is a consequence of the discrete Fourier transform.

Figure 5

(Color online) (a) Obtained yield for the process $|L⟩\to |R⟩$ as a function of the field length. (b) Yield for the same process as a function of the fluence for three field lengths.

Figure 6

(Color online) Optimized field (upper panel) for the fivefold charge–switch process $|L⟩\to |R⟩\to |L⟩\cdots \to |R⟩$ (lower panel) in a double quantum dot. Here we have used a threshold frequency of ${\omega }_{\text{th}}=0.817$ leading to the target state occupation of 99.46% at the end of the total fivefold process.