The Experimental Observation of Beliaev Damping in a Bose Condensed Gas

We report the first experimental observation of Beliaev damping of a collective excitation in a Bose-condensed gas. Beliaev damping is not predicted by the Gross-Pitaevskii equation and so this is one of the few experiments that tests BEC theory beyond the mean field approximation. Measurements of the amplitude of a high frequency scissors mode, show that the Beliaev process transfers energy to a lower lying mode and then back and forth between these modes. These characteristics are quite distinct from those of Landau damping , which leads to a monotonic decrease in amplitude. To enhance the Beliaev process we adjusted the geometry of the magnetic trapping potential to give a frequency ratio of 2 to 1 between two of the scissors modes of the condensate. The ratios of the trap oscillation frequencies ωy/ωx and ωz/ωx were changed independently, so that we could investigate the resonant coupling over a range of conditions. In the Beliaev damping process [1], one quantum of excitation converts into two quanta of a lower frequency mode, in a manner analogous to parametric down-conversion of light in nonlinear media. This process occurs readily in a homogeneous system such as super-fluid helium where there are many very closely spaced low-lying energy levels. However, it has not previously been observed for a trapped Bose-condensed gas, which has discrete modes with well-resolved excitation energies. We have observed the Beliaev process for a scissors mode [3] of a BEC of rubidium atoms, when the mode resonantly couples to another mode at half its frequency. Beliaev damping can be regarded as a four wave mixing process, in which a Bogoliubov quasiparticle interacts with the ground state component of the condensate to produce two new quasiparticles that share the initial energy equally. At zero temperature, only Beliaev damping may occur, whilst at finite temperature Landau damping is the primary mechanism which dissipates the energy of collective excitation into the thermal cloud [4]. Landau damping corresponds to a scattering process between two quasi-particles in the initial mode, which results in one particle gaining all of the energy and the other going into the condensate ground state. The Landau damping rate and its strong dependence on temperature has been measured for two of the quadrupole excitations of the con-densate [5]. We observe a comparable Landau damping rate for the scissors mode in most trap geometries, except those where the frequencies of the two scissors modes …