  We present a combined analytical and numerical study for coherent terahertz
control of a single molecular polariton, formed by strongly coupling two
rotational states of a molecule with a single-mode cavity. Compared to the bare
molecules driven by a single terahertz pulse, the presence of a cavity strongly
modifies the post-pulse orientation of the polariton, making it difficult to
obtain its maximal degree of orientation. To solve this challenging problem
toward achieving complete quantum coherent control, we derive an analytical
solution of a pulse-driven quantum Jaynes-Cummings model by expanding the wave
function into entangled states and constructing an effective Hamiltonian. We
utilize it to design a composite terahertz pulse and obtain the maximum degree
of orientation of the polariton by exploiting photon blockade effects. This
work offers a new strategy to study rotational dynamics in the strong-coupling
regime and provides a method for complete quantum coherent control of a single
molecular polariton. It, therefore, has direct applications in polariton
chemistry and molecular polaritonics for exploring novel quantum optical
phenomena.
