Quantum state engineering for multiple hot trapped ions in the symmetric Dicke subspace
We propose a scheme for the generation of an arbitrary quantum states for multiple trapped ions in the symmetric Dicke subspace. One can manipulate the collective ion transition in a selective symmetric Dicke subspace via the virtual excitation induced inequidistant energy levels. All the states undergo the same phonon number dependent Stark shift and thus the scheme is insensitive to the thermal motion. Furthermore, the scheme does not require individual addressing of the ions.