It is demonstrated that the time evolution of the heteronuclear polari
zation-transfer process in a dipolar-coupled nuclear spin system can b
e reversed, leading to the observation of cross polarization echoes. T
he cross-polarization echoes are induced by consecutive application of
two pulse trains that produce effective Hamiltonians that differ only
in sign, Cross-polarization echoes have been recorded for a powder sa
mple of alanine. The time evolution of the spin;system is consistent w
ith both unitary quantum dynamics and with spin thermodynamics of two
systems approaching a common spin temperature. (C) 1998 American Insti
tute of Physics.