Formation of Wigner Crystals in Ion Traps

Similar to the situation for a coupled pendulum, normal vibrations can be excited in a Wigner crystal. For example, the two-ion crystal has two normal vibrations where the two ions oscillate in the ion trap potential either in phase or with opposite phases. For the in-phase oscillations, the Coulomb repulsion between the ions does not influence the oscillation frequency because the distance between the 

If several ions are trapped in an ion trap and are cooled by optical sideband cooling, a phase transition may occur at the temperature T. where the ions arrange into a stable, spatially symmetric configuration like in a crystal [14.68-71]. The distances between the ions in this Wigner crystal are about 10 -10 times larger than those in an ordinary ion crystal such as NaCl. 

This phase transition from the statistically distributed ions in a gaseous cloud to an ordered Wigner crystal can be monitored by the change in the fluorescence intensity. This is observed as a function of the detuning Aw of the cooling laser. The distribution IpiCAw) has a completely different shape for the ordered state of the Wigner crystal than for the disordered ion cloud (Fig. 14.24). 

These vibrational modes can be excited if an additional AC voltage with the proper frequency is applied to the trap electrodes. The excitation 

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