  We propose and demonstrate an echo method to reduce the inhomogeneous
linewidth of Bogoliubov excitations, in a harmonically-trapped Bose-Einstein
condensate. Our proposal includes the transfer of excitations with momentum +q
to -q using a double two photon Bragg process, in which a substantial reduction
of the inhomogeneous broadening is calculated. Furthermore, we predict an
enhancement in the method's efficiency for low momentum due to many-body
effects. The echo can also be implemented by using a four photon process, as is
demonstrated experimentally.
