We generate half-excited symmetric Dicke states of two and four ions. We usemulti-level stimulated Raman adiabatic passage (STIRAP) whose intermediatestates are phonon Fock states. This process corresponds to the spin squeezingoperation and half-excited Dicke states are generated during multi-levelSTIRAP. This method does not require local access for each ion or thepreparation of phonon Fock states. Furthermore, it is robust since it is anadiabatic process. We evaluate the Dicke state using a witness operator anddetermine the upper and lower bounds of the fidelity without using full quantumtomography.
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