Breathing Mode of an Anharmonically Trapped One-Dimensional Bose Gas

We theoretically investigate the breathing frequency of a one-dimensional ultra-cold atomic Bose gas in the weakly and strongly interacting regimes. In view of the relevant experimental conditions, the trap considered in this work is a quadratic plus quartic potential. The local chemical potential of the Bose gas is calculated with the Lieb–Liniger model, and the equation of motion for the width of the gas is derived by using a variational approach. The breathing frequency is strongly affected by the anharmonic distortion in the strongly interaction regime while it is insensitive to the anharmonic distortion in the weakly interacting regime.