Quantum Lyapunov Control Based on the Average Value of an Imaginary Mechanical Quantity
For quantum control researchers, it addresses the limitation of single-control methods that only converge to a set, but the extension is incremental.
The paper extends quantum Lyapunov control to multi-control Hamiltonian systems, proving convergence to desired target states even in degenerate cases, with numerical verification on a three-level system.
The convergence of closed quantum systems in the degenerate cases to the desired target state by using the quantum Lyapunov control based on the average value of an imaginary mechanical quantity is studied. On the basis of the existing methods which can only ensure the single-control Hamiltonian systems converge toward a set, we design the control laws to make the multi-control Hamiltonian systems converge to the desired target state. The convergence of the control system is proved, and the convergence to the desired target state is analyzed. How to make these conditions of convergence to the target state to be satisfied is proved or analyzed. Finally, numerical simulations for a three level system in the degenrate case transfering form an initial eigenstate to a target superposition state are studied to verify the effectiveness of the proposed control method.