Preparation Of Continuous-variable Cluster States Created By Atomic Ensembles In Optical Cavity

Continuous-variable(CV) cluster state quantum computation is a highly interesting and active field because it provides a new outlook on quantum information and quantum com-putation. Cluster states, which were known as a class of highly entangled multipartite states, their interaction only exists between adjacent mode. In recent years, quantum com-munication, or more generally quantum information with CV cluster state, has attracted a lot of interest and appears to yield very promising perspectives concerning both experi-mental realizations and general theoretical insights, due to its relative simplicity and high efficiency in the generation, manipulation, and detection of the CV state.In this paper, we present two kinds of schemes to generate CV entangled cluster states. The model of the first scheme is six atomic ensembles located in a hexagonal single-mode cavity, with the appropriate selections of squeezing parameters and pump laser parameter-s,coupling between atomic ensemble and the cavity mode occurs, via six steps the linear and square six-mode CV cluster state will be successfully prepared.The other one is to prepare a specific four-mode ring weighted CV cluster state,which has been utilized by Zhang to explain how quantum teamwork works. We will show that for just once choice about the appropriate squeezing parameters and pump laser param-eters, with the special squeezing operator and a new unitary transformation can steer the atomic ensembles into a stationary four-mode squeezed vacuum via cavity dissipation. Both schemes with some approximations which lead to the ignorance of the atomic spon-taneous emission, the Hamiltonian is transformed into the effective Hamiltonian which only contains the coupling between two ground states and the cavity mode, via the cavity field dissipation and choosing the appropriate squeezing parameters, Rabi frequencies and phases of lasers, which can steer the atomic ensembles into the prospective multimode CV cluster states.