Heat rectification with a minimal model of two harmonic oscillators

We study heat rectification in a minimalistic model composed of two unequal atoms subjected to linear forces and in contact with effective Langevin baths induced by Doppler lasers. Analytic expressions of the heat currents in the steady state are spelled out. Asymmetric heat transport is found in this linear system if both the bath temperatures and the temperature-dependent bath-system couplings are exchanged. The model can be realized with two ions in either common or individual traps. This physical setting allows for a natural temperature dependence of the coupling to the baths. We also explore the parameter space of the model to optimize asymmetric heat current and find conditions for maximal rectification. High rectification corresponds to a good match of the power spectra of the ions for forward temperature bias and mismatch for reverse bias, which may be understood by the behavior of dissipative normal modes.