  Dissipation is often considered as a detrimental effect in quantum systems
for unitary quantum operations. However, it has been shown that suitable
dissipation can be useful resources both in quantum information and quantum
simulation. Here, we propose and experimentally simulate a dissipative phase
transition (DPT) model using a single trapped ion with an engineered reservoir.
We show that the ion's spatial oscillation mode reaches a steady state after
the alternating application of unitary evolution under a quantum Rabi model
Hamiltonian and sideband cooling of the oscillator. The average phonon number
of the oscillation mode is used as the order parameter to provide evidence for
the DPT. Our work highlights the suitability of trapped ions for simulating
open quantum systems and shall facilitate further investigations of DPT with
various dissipation terms.
