Quantum Simulations with a Trilinear Hamiltonian

TL;DR

This paper experimentally implements a trilinear Hamiltonian among three ion motion modes to simulate quantum optical interactions like atom-light coupling and parametric down conversion.

Contribution

It demonstrates the first experimental realization of a trilinear Hamiltonian in a trapped-ion system in the strong-coupling regime.

Findings

Successful simulation of atom-light interaction using the trilinear Hamiltonian

Implementation of nondegenerate parametric down conversion in ion traps

Strong-coupling regime achieved with high fidelity

Abstract

Interaction among harmonic oscillators described by a trilinear Hamiltonian $\hbar \xi (a^{\dagger} b c + a b^{\dagger} c^{\dagger}$) is one of the most fundamental models in quantum optics. By employing the anharmonicity of the Coublomb potential in a linear trapped three-ion crystal, we experimentally implement it among three normal modes of motion in the strong-coupling regime, where the coupling strength is much larger than the decoherence rate of the ions motion. We use it to simulate the interaction of atom and light as described by the Tavis-Cummings model and the process of nondegenerate parametric down conversion in the regime of depleted pump.