Multipartite entanglement of three trapped ions in a cavity and W state generation
A scheme to generate three qubit maximally entangled W states, using three trapped ions interacting with the red sideband tuned single mode field of a high finesse cavity, is proposed. For the cavity field initially prepared in a number state, the probability of generating the three ion W state is calculated. By using the ion cavity coupling strengths achieved in experimental realizations, the interaction time needed for W state generation is found to be of the order of 10 us. It is found that for a fixed number of photons in the cavity the nature of entanglement of ionic internal states can be manipulated by an appropriate choice of the initial state phonon number. The ionic qubits in the W like state are found to be entangled to cavity photons. Analytical expressions for global negativity and partial K way negativities (K 2 to 4) are obtained to study the evolution of entanglement distribution as a function of the interaction parameter. Reversible entanglement exchange between different entanglement modes is observed. For specific values of the interaction parameter, the three ions and photon phonon system are found to have 4 partite entanglement, generated by 2 way and 3 way correlations.