# Applications of the trilinear Hamiltonian with three trapped ions

Friday, December 1, 2017 — 3:00 PM EST

## Roland Esteban Hablützel Marrero, Centre for Quantum Technologies, National University of Singapore

Three coupled harmonic oscillators with an interaction given by the trilinear Hamiltonian $a^{\dagger} b c + a b^{\dagger} c^{\dagger}$ can describe a wide range of physical processes. In this talk I will show how we implement the trilinear Hamiltonian utilizing a chain of three $^{171}$Yb$^+$ ions in a linear Paul trap. We are able to experimentally realize such an interaction Hamiltonian among three normal modes of motion represented by the annihilation operators $a$, $b$, and $c$. The interaction arises naturally as a consequence of the ions' anharmonic mutual Coulomb repulsion, but it is only dominant when the system fulfills a resonance condition, which is equivalent to energy conservation. The system can be brought into/out of resonance at will by adjusting the trapping frequencies. With this implementation, we are able to simulate various physical models such as the non-degenerate parametric down conversion in a regime of depleted pump, the Jaynes-Cummings model, and a simple model of Hawking radiation. Moreover, motivated by the recent interest in quantum thermal engines, I will show our experimental realization of a quantum absorption refrigerator using this system. We investigate the dynamical and steady state properties of this refrigerator after preparation of thermal states, and, furthermore, analyze the cooling capabilities when squeezing is employed as a quantum resource. We also study the performance of the refrigerator in the single shot regime, and demonstrate cooling below both the steady-state energy and that predicted by the ideal adiabatic operation.

Location
QNC - Quantum Nano Centre
1201
200 University Avenue West

Waterloo, ON N2L 3G1
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