Towards homogeneously broadened spectroscopy of bogoliubov excitations in bose condensates

This study proposes and demonstrates experimentally a momentum space echo method using two and four-photon Bragg pulses, in order to overcome Doppler broadening and inhomogeneous density effects. This method involves of an excitation scheme which results to populations in momentum space. This scheme is demonstrated experimentally by using a four-photon echo pulse to reflect the initially populated excitations. The spectroscopic response of the echo pulse is narrower than that of a regular Bragg pulse. This study also determines the high resolution Bragg spectrum of a BEC in a harmonic trap. Results show that the Bragg spectrum contains radial modes due to the inhomogeneity and finite size of the BEC in the radial dimension. Here, steeper external trapping potentials in the radial dimension is considered, and a suppression of the number of excited radial modes is calculated, as compared to harmonic trapping, using the quasi-particle projection method. In the limit of a box potential, a single excited mode is found. For linear excitations beyond the phonon regime, an effective potential representation of the problem is presented, which limits the number of excited modes by calculating the number of trapped states of this potential. By making the trap steeper, modes are driven out of the trapped state region, and eventually are left with only one mode which is excited significantly