Ultrafast manipulation of a double quantum dot via Lyapunov control method

For a double quantum dot (DQD) system, we propose a Lyapunov control method to transfer the state from initial state to the target state on the picosecond scale, which open a significant new area of research for the system control theories. The control laws are composed of two-direction components, one is used to eliminate the dissipation in the system, another is used to transfer the state. The Lyapunov stability theorem ensures the system can be transferred to the target state in high probability, and the coefficients in control laws leads very fast convergence. The role of eliminating the dissipation plays the suppression of decoherence effect. Numerical simulation results show that the transfer probability and fidelity can be increased up to 98.79% and 98.97%, respectively. This is the first result directly applicable to a DQD system´s state transferring using the Lyapunov control method. We also give specific experimental realization scheme.