Probing a Dissipative Phase Transition with a Trapped Ion through Reservoir Engineering

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