Fast preparation of Bell state and W state with Rydberg superatom

In the paper, we propose a scheme for fast preparation of Bell state and W state based on quantum Zeno dynamics and shortcuts to adiabaticity with Rydberg superatom. The quantum information is encoded in the collective state of superatom which contains n individual ladder-type Rydberg atoms. When the Rabi frequencies of classical fields are appropriately regulated, the scheme can be achieved within one step. Moreover, the effects of imperfections induced by leakage of the cavity and atomic spontaneous emission are also taken into account. The numerical simulation result shows that this scheme is robust against both cavity leakage and atomic spontaneous emission.