  We predict a mechanism for achieving complete population inversion in a
continuously driven InAs/GaAs semiconductor quantum dot featuring $V$-type
transitions. This highly nonequilibrium steady state is enabled by the
interplay between $V$-type interband transitions and a non-Markovian
decoherence mechanism, introduced by acoustic phonons. The population trapping
mechanism is generalized to a chain of coupled emitters. Exploiting the
population inversion, we predict unidirectional excitation transport from one
end of the chain to the other without external bias, independent of the unitary
interdot coupling mechanism.
