  We show that the quantum phase transition of the Tavis-Cummings model can be
realised in a linear ion trap of the kind proposed for quantum computation. The
Tavis-Cummings model describes the interaction between a bosonic degree of
freedom and a collective spin. In an ion trap, the collective spin system is a
symmetrised state of the internal electronic states of N ions, while the
bosonic system is the vibrational degree of freedom of the centre of mass mode
for the ions.
