Correlated collective excitation and quantum entanglement between two Rydberg superatoms in the steady state

Owing to the unique physical characteristics of Rydberg atoms, which play an important role in quantum information and quantum computation, the theoretical and applied research of Rydberg atoms have become one of the hot spots of scientific research in recent years. Thanks to the large polarizability of Rydberg atoms, even a small electric field could cause a considerable electric dipole moment, resulting in a strong dipole-dipole interaction between Rydberg atoms. The multiple excitations of the Rydberg states are strongly inhibited because of the strong dipole interaction between atoms within a mesoscopic interaction (blockade) region. We call this phenomenon the dipole blockade effect. The dipole blockade regime allows us to build single-photon quantum devices, implement quantum gates, generate quantum entanglement, simulate many-body quantum problems and so on.A Rydberg atomic ensemble in the same blockade region can be regarded as a superatom. In the same way, if these atoms trapped in two optical dipole traps, each sub-ensemble can be considered as a sub-superatom which is closely related to the superatom. Based on the fact that two Rydberg sub-superatoms will be strongly correlated due to sharing no more than one excited Rydberg atom, we study the correlated collective excitation and the quantum entanglement between two Rydberg sub-superatoms in the steady state. With the superatom model, the problem of exponentially increasing system size with the number of atoms can be circumvented to a certain extent in studying many-body physics. By solving the two body Lindblad's master equation accurately, we obtain the analytical expressions for the collective excitation probabilities of the two sub-superatoms, and the concurrence measuring the bipartite entanglement between them. Our results show that they are all sensitive to the number of each Rydberg superatom:the bigger (including more atoms) the Rydberg superatom, the higher the collective Rydberg excitation probability; the maximally entangled state can only be obtained with two equal-sized Rydberg superatoms. When this condition is fulfilled, the generation of mesoscopic entanglement could be achieved by adding the number of each Rydberg superatom. This may provide an attractive platform to study the quantum-classical correspondence and have potential promising applications in quantum information processing.