Quantum Simulations with a Trilinear Hamiltonian

Abstract

Interaction among harmonic oscillators described by a trilinear Hamiltonian $\hslash \xi (a^{†}bc+a{b}^{†}{c}^{†}$) 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.

arXiv comment5 pages, 3 figures

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• Hybrid quantum computation gate with trapped ion system
• Programmable quantum simulations of bosonic systems with trapped ions
• Quantum computation and simulation with vibrational modes of trapped ions
• Nonclassicality detection from few Fock-state probabilities
• Numerical studies of back-reaction effects in an analog model of cosmological pre-heating
• Pump Depletion in Parametric Amplification
• Quantum non-Gaussian Photon Coincidences
• Phase effects in coherently-stimulated down-conversion with a quantized pump field
• Entanglement growth via splitting of a few thermal quanta
• Quantum parameter estimation of nonlinear coupling in trilinear Hamiltonian with trapped ions
• Optimal quantum sensing of the nonlinear bosonic interactions using Fock states
• Unconditional remote entanglement using second-harmonic generation and twin two-mode squeezed vacuum states
• Nonlinear stochastic and quantum motion from Coulomb forces