Optimal Control of Quantum Rings by Terahertz Laser Pulses

Complete control of single-electron states in a two-dimensional semiconductor quantum-ring model is established, opening a path into coherent laser-driven single-gate qubits. The control scheme is developed in the framework of optimal-control theory for laser pulses of two-component polarization. In terms of pulse lengths and target-state occupations, the scheme is shown to be superior to conventional control methods that exploit Rabi oscillations generated by uniform circularly polarized pulses. Current-carrying states in a quantum ring can be used to manipulate a two-level subsystem at the ring center. Combining our results, we propose a realistic approach to construct a laser-driven single-gate qubit that has switching times in the terahertz regime.

Figure 1

(a) Shape of the external confining potential for a quantum ring and an example of a circularly polarized laser field. (b) Energy-level spectrum of a quantum ring. The transitions are allowed along the dashed line so that $\Delta l=\pm 1$.

Figure 2

(a) Components ${ϵ}_x(t)$ [blue (dark gray)] and ${ϵ}_y(t)$ [red (light gray)] of the optimized (solid lines) and uniform laser pulses (dashed lines) for $|1⟩\to |2⟩$ transition. (b) Spectrum of the optimized field. The dashed lines correspond to eigenfrequencies ${\omega }_{12}$ and ${\omega }_{23}$.

Figure 3

Maximum occupation of the target state in transition $|1⟩\to |2⟩$ as a function of the pulse length. The open (blue) circles correspond to continuous waves and the filled (red) circles to the optimal-control result. The insets show the densities $|\Psi (T=100){|}^2$ when the corresponding achieved occupations are 0.99 and 0.9998 for these pulse types, respectively.

Figure 4

Schematic picture of transitions from $l=-1$ to $l=1$ (a) and from $l=-2$ to $l=2$ (b) (upper panel), optimized fields for these transitions (middle panel), and the occupations of the states (lower panel).

Figure 5

Time-dependent electron density $|\Psi (\mathbf{r},t){|}^2$ [light shade (yellow), low; black, high] and the current $\mathbf{j}(\mathbf{r},t)$ (arrows) at different times in the transition from $l=-1$ to $l=1$ driven by the optimized pulse [see Fig. 4a].