Generation of Three-Atom Singlet State with High-Fidelity by Lyapunov Control

An effective protocol is proposed to generate three-atom singlet states in an atom-cavity coupled system. By analyzing the interactions between atoms and cavity, we first derive a Hamiltonian with the target singlet state approximatively being one of its eigenstates. Then, to drive the system from the initial state to the target state, we design the waveform of the external laser fields by Lyapunov control method. The parameter selections are discussed based on the experimentally available parameters, and the influence of the errors and decoherence on the fidelity are analyzed. Numerical simulations indicate that the protocol can not only generate singlet-state with high speed, but also possess great robustness against operational errors and decoherence. Therefore, the protocol may be useful in the singlet-state-based quantum information processing.