Permanent Directional Heat Currents in Lattices of Optomechanical Resonators

We study the phonon dynamics in lattices of cavity-coupled optomechanical resonators where the mutually coupled photonic modes are coherently driven and the mechanical resonators are uncoupled and connected to independent thermal baths.
We present a general procedure to obtain the effective Lindblad dynamics of the phononic modes for an arbitrary lattice geometry, where the light modes play the role of an effective reservoir that mediates the phonon nonequilibrium dynamics. In our picture, quantum fluctuations of the optical fields mediate effective long-range interactions between mechanical sites of both coherent and dissipative nature, whose range is tunable via the correlation length of the reservoir.
We show how to stabilize stationary states exhibiting directional heat currents over arbitrary distance, despite the absence of thermal gradient and of direct coupling between the mechanical resonators.

[1] Zakari Denis, Alberto Biella, Ivan Favero, and Cristiano Ciuti, Phys. Rev. Lett. 124, 083601 (2020)