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Bulletin of the American Physical Society

Engineering a Trapped Ion Open-System Dicke Model with Dissipative Phase Transitions

Florentin Reiter, Malte D. Dueholm, Anders Søndberg Sørensen, Susanne F. Yelin

Published Jun 6, 2017• 0 citations
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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 in both 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.
The Dicke model, which describes the coupling of an ensemble of spins to a harmonic oscillator, is known for its superradiant phase transition, which can both be observed in the ground state in a purely Hamiltonian setting, as well as in the steady state of an open-system Dicke model with dissipation. We demonstrate that, in addition, the dissipative Dicke model can undergo a second phase transition to a nonstationary phase, characterized by unlimited heating of the harmonic oscillator. Identifying the mechanism of the phase transition and deriving the scaling of the critical coupling with the system size we conclude that the novel phase transition can be understood as a cooperative breakdown of the oscillator blockade which otherwise prevents higher excitation of the system. We discuss an implementation with trapped ions and investigate the role of cooling, by which the breakdown can be suppressed.
We use a self-assembled two-dimensional Coulomb crystal of ∼70 ions in the presence of an external transverse field to engineer a simulator of the Dicke Hamiltonian, an iconic model in quantum optics which features a quantum phase transition between a superradiant (ferromagnetic) and a normal (paramagnetic) phase. We experimentally implement slow quenches across the quantum critical point and benchmark the dynamics and the performance of the simulator through extensive theory-experiment comparisons which show excellent agreement. The implementation of the Dicke model in fully controllable trapped ion arrays can open a path for the generation of highly entangled states useful for enhanced metrology and the observation of scrambling and quantum chaos in a many-body system.