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Bulletin of the American Physical Society

Quantum simulations with a trilinear Hamiltonian in trapped-ion system

Shiqian Ding, Gleb Maslennikov, Roland Hablützel, Dzmitry Matsukevich

Published May 26, 2016• 0 citations
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Interaction among harmonic oscillators described by a trilinear Hamiltonian $\ensuremath{\hbar}\ensuremath{\xi}({a}^{\ifmmode\dagger\else\textdagger\fi{}}bc+a{b}^{\ifmmode\dagger\else\textdagger\fi{}}{c}^{\ifmmode\dagger\else\textdagger\fi{}})$ is one of the most fundamental models in quantum optics. By employing the anharmonicity of the Coulomb 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 ion motion. We use it to simulate the interaction of an atom and light as described by the Tavis-Cummings model and the process of nondegenerate parametric down-conversion in the regime of a depleted pump.
We study the quantum and classical evolution of a system of three harmonic modes interacting via a trilinear Hamiltonian. With the modes prepared in thermal states of different temperatures, this model describes the working principle of an absorption refrigerator that transfers energy from a cold to a hot environment at the expense of free energy provided by a high-temperature work reservoir. Inspired by a recent experimental realization with trapped ions, we elucidate key features of the coupling Hamiltonian that are relevant for the refrigerator performance. The coherent system dynamics exhibits rapid effective equilibration of the mode energies and correlations, as well as a transient enhancement of the cooling performance at short times. We find that these features can be fully reproduced in a classical framework.