How to measure the Bogoliubov quasiparticle amplitudes in a trapped condensate

We propose an experiment, based on two consecutive Bragg pulses, to measure the momentum distribution of quasiparticle excitations in a trapped Bose gas at low temperature. With the first pulse one generates a bunch of excitations carrying momentum $q$, whose Doppler line is measured by the second pulse. We show that this experiment can provide direct access to the amplitudes $u_{q}$ and $v_{q}$ characterizing the Bogoliubov transformations from particles to quasiparticles. We simulate the behavior of the nonuniform gas by numerically solving the time dependent Gross-Pitaevskii equation.