  We introduce a new thermal transport phenomenon, a unidirectional
selection-rule blockade, and show how it produces unprecedented rectification
of bosonic heat flow through molecular or mesoscopic quantum systems.
Rectification arises from the quantization of energy levels of the conduction
element and selection rules of reservoir coupling operators. The simplest
system exhibiting the selection-rule blockade is an appropriately coupled
three-level system, providing a candidate for a high-performance heat diode. We
present an analytical treatment of the transport problem and discuss how the
phenomenon generalizes to multilevel systems.
