Rapid Preparation of Rydberg Superatom W State Using Superadiabatic Techniques

The W state, as a robust multipartite entangled state, plays an important role in quantum information processing, quantum network construction and quantum computing. In this paper, the three-level ladder-type Rydberg atomic system is put into the Rydberg blocking ball to form a superatom. Each superatom has many collective states including just one Rydberg excitation constrained by the Rydberg blockade effect. In the weak cavity field limit, at most one atom can be pumped into excited state, then we can describe the superatom by a three-level ladder-type system. Afterwards we encode quantum information on the effective energy levels of Rydberg superatoms and propose a fast scheme for preparing the Rydberg superatom W state based on the superadiabatic iterative technique and quantum Zeno dynamics, this scheme can be achieved in only one step by controlling the laser pulses. In the current scheme, the superatoms are trapped in spatially separated cavities connected by optical fibers, which significantly enhances the feasibility of experimental manipulation. A remarkable feature is that it does not require precise control of experimental parameters and interaction time. Meanwhile, the form of counterdiabatic Hamiltonian is the same as that of the effective Hamiltonian. Through numerical simulations, the fidelity of this scheme can reach 99.94$\%$. Even considering decoherence effects, including atomic spontaneous emission and photon leakage, the fidelity can still exceed 97.5$\%$, further demonstrating the strong robustness of the solution. In addition, the Rabi frequency can be characterized as a linear superposition of Gaussian functions, this representation significantly alleviates the complexity encountered in practical experiments. Futhermore, we also analyzed the impact of parameter fluctuations on the fidelity, the results show that this scheme is robust against parameter fluctuations. At last, the present scheme is extended to the cases of $N$ Rydberg superatoms, which shows the scalability of our scheme.