Selective control of the symmetric Dicke subspace in trapped ions

We propose a method of manipulating selectively the symmetric Dicke subspace in the internal degrees of freedom of $N$ trapped ions. We show that the direct access to ionic-motional subspaces, based on a suitable tuning of motion-dependent ac Stark shifts, induces a two-level dynamics involving previously selected ionic Dicke states. In this manner, it is possible to produce, sequentially and unitarily, ionic Dicke states with increasing excitation number. Moreover, we propose a probabilistic technique to produce directly any ionic Dicke state assuming suitable initial conditions.

Figure 1

$N$ three-level ions in a linear Paul trap where the energy diagram of the $j\text{th}$ ion is displayed.