Echo spectroscopy of bulk Bogoliubov excitations in trapped Bose-Einstein condensates

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.