High fidelity Dicke-state generation with Lyapunov control in circuit QED system

In this paper, we propose a scheme to generate highly entangled Dicke-state in circuit quantum electrodynamics (QED) system, where the quantum tunneling between local potential wells is manipulated by using Lyapunov control. We employ two different types of control Hamiltonians to generate Dicke-state: one is the local Hamiltonian that requires to individually modulate control fields; the other is the global Hamiltonian (global control) where the control fields can be modulated uniformly. Furthermore, the target Dicke-state can be obtained with arbitrary initial states when applying the average-value-based Lyapunov control. Numerical simulations demonstrate that the generation of Dicke-state is remarkably accelerated by using bang-bang Lyapunov control, and the multipartite Dicke-state is implemented at nanoseconds without accurately controlling the evolution time in ultrastrong coupling regime. In addition, the scheme is robust against some kinds of uncertainties and perturbations.