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Quantum phase transitions (QPTs) are usually associated with many-bodysystems with large degrees of freedom approaching the thermodynamic limit. Insuch systems, the many-body ground state shows abrupt changes at zerotemperature when the control parameter of the Hamiltonian is scanned across aquantum critical point. Recently it has been realized that a QPT can also occurin a simple system composed of only a two-level atom and a single-mode bosonicfield, described by the quantum Rabi model (QRM). Here we report the firstexperimental demonstration of a QPT in the QRM using a single trapped ion. Wemeasure the average spin-up state population of the ion and the average phononnumber in its spatial oscillation mode as two order parameters and observe theclear evidences of the phase transition via slow quench of the coupling betweenthe ion and its spatial motion. An experimental probe of the phase transitionsin a fundamental quantum optics model without imposing the thermodynamic limitopens up a new window for the controlled study of QPTs and quantum criticalphenomena.

Observation of a quantum phase transition in the quantum Rabi model with a single trapped ion