Conditional generation of highly excited Dicke states for N atoms via a single asymmetric atom-cavity interaction

We propose a scheme for the generation of highly excited Dicke states for multiple atoms. In the scheme N + 1 atoms dispersively interact with a vacuum cavity, with the last atom having a different coupling and driven by a classical field. As the first N atoms are symmetric, they remain in the symmetric Dicke subspace, with the spacing of energy levels being unequal due to the vacuum light shift. Employing the Stark shift induced by the classical field, one can tune the last atom in resonance with the transition between two specific Dicke states of the first N atoms. So the detection of the state of the last atom conditionally collapses the first N atoms to the desired Dicke state.