Quantum and classical dynamics of a three-mode absorption refrigerator

Stefan Nimmrichter1, Jibo Dai1,2, Alexandre Roulet1,3, and Valerio Scarani1,4

1Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543
2Data Storage Institute, A*STAR, Singapore
3Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
4Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117542

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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.

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