We explore the energy dynamics of a two dimensional (2D) trapped Bose-Einstein condensate (BEC) excited by a moving red-detuned laser potential (RDLP). The trap is a combination of a power-law (PL) potential cutoff by a hard-wall box potential (HWBP). It is found that by a restricted measurment of the energy within the boundaries of the HWBP, the energy demonstrates oscillations indicative of solitons. It is then demonstrated, that the geometry of the PL potential influences the lifetime of these oscillations, i.e., the lifetime of the ensuing solitons inside the HWBP. We argue that the energy dynamics in this setup are a good tool for measuring their lifetime. It is also found, that the condensate density dynamics display oscillatory patterns of a magnitude and order controlled by the velocity of the RDLP. A connection to oscillations in the chemical potential dynamics is also discussed. Essentially, we suggest future experiments for this kind of setup, which would measure the phonon energy dynamics to trace the lifetime of solitons.
We explore the energy dynamics of a two dimensional (2D) harmonically trapped Bose-Einstein condensate inside a box potential, excited by a moving red-detuned laser potential (RDLP). For an RDLP velocity
v less than a critical value
vc, energy oscillations are observed to begin simultaneously with the motion of the RDLP. For
v>vc, these oscillations are delayed through a transient in the energy. At the end of the delay time
tons, the energy oscillations are regenerated again, and
tons is found to depend on
v through universal relations for two cases: one for an RDLP depth sufficient to break off a BEC fragment, another for a depth insufficient to split the BEC. In the case of splitting,
tons exactly equals the time it takes the BEC fragment (dragged by the RDLP trough) to reach the hard wall of the box potential.