  There has been significant interest recently in using complex quantum systems
to create effective nonreciprocal dynamics. Proposals have been put forward for
the realization of artificial magnetic fields for photons and phonons;
experimental progress is fast making these proposals a reality. Much work has
concentrated on the use of such systems for controlling the flow of signals,
e.g., to create isolators or directional amplifiers for optical signals. In
this paper, we build on this work but move in a different direction. We develop
the theory of and discuss a potential realization for the controllable flow of
thermal noise in quantum systems. We demonstrate theoretically that the
unidirectional flow of thermal noise is possible within quantum cascaded
systems. Viewing an optomechanical platform as a cascaded system we here that
one can ultimately control the direction of the flow of thermal noise. By
appropriately engineering the mechanical resonator, which acts as an artificial
reservoir, the flow of thermal noise can be constrained to a desired direction,
yielding a thermal rectifier. The proposed quantum thermal noise rectifier
could potentially be used to develop devices such as a thermal modulator, a
thermal router, and a thermal amplifier for nanoelectronic devices and
superconducting circuits.
