Experimental progress towards dissipative phase transition in quantum spin model using trapped ions

Dissipative phase transitions (DPTs) is an important phenomenon in non-equilibrium driven dissipative systems beyond thermal equilibrium. Trapped ion platforms are well suited for such studies due to their long coherence times, high fidelity control, and precisely programmable dissipation. Here, we report experimental progress toward realizing DPT in transverse-field Ising model using a chain of Ca+ ions. Qubits are encoded in the electronic ground state, with effective spin–spin interactions engineered via coupling to collective motional modes. Controllable dissipation is implemented using a drive-reset protocol through metastable states. As an immediate step, we experimentally characterize the competition between coherent interactions and dissipation in a single qubit across a wide range of dissipation strengths, by measuring time evolutions and comparing them with an effective two-level Lindblad equation. In addition, we establish other key experimental capabilities to simulate such many-body systems, including site-resolved spin readout of up to 24 qubits, magnetic field gradient compensation, and mid-circuit shelving for two-time correlation measurements. On the theory side, we study the impact of realistic experimental imperfections including Trotterization errors, motional mode heating, and photon recoil heating induced by dissipation, to assess their influence on steady state properties and critical signatures. These results pave the way toward realizing a broad class of DPTs and dissipative quantum state engineering with trapped ions.