Wadkin-Snaith, Dominic Carl (2012)
Ph.D. thesis, University of Birmingham.
This thesis deals with grey soliton dynamics in confining potentials and their association with the trapped Lieb II mode. There has been a large body of work into the study of grey solitons and their dissipation in ultra cold trapped Bose gases. It is well known at finite temperature that the standard mechanism for soliton decay in uniform ultra cold gases is scattering of thermal phonons, where the soliton lifetime was found to be proportional to inverse temperature for temperatures greater than the chemical potential . The scattering of thermal phonons becomes no longer efficient for the exactly integrable Gross-Pitaevski equation. The case of non-integrable interactions has been considered and for this case the lifetime of the soliton was found to diverge as the inverse fourth power of temperature T. Thus solitons propagating in a uniform background are found to be stable at zero temperature.
In the presence of a trapping potential, momentum conservation is lost due to the loss of translational invariance and this leads to soliton decay even at zero temperature. Classically it has been shown that as long as the confinement is slowly varying on the length scale of the soliton then conservative dynamics are found , .
To extend previous findings we use the Born-Sommerfeld rule to quantise the grey soliton in any smooth potential with one minimum. We find a ladder of energy levels for the case of harmonic confinement and associate these states with the trapped Lieb 11 mode. These trapped Lieb 11 states are not eigenstates but are to be considered as quasiparticle resonances. The finite lifetime is due to the radiation of phonons by an accelerating grey soliton, we are able to calculate this lifetime in the semiclassical limit. We show that for a large number of trapped atoms that the quasiparticle states are long lived and can be resolved experimentally.
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