Quantum Phase Transitions in a Linear Ion Trap

Abstract

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.