Nonlinear resonance phenomenon of one-dimensional Bose–Einstein condensate under periodic modulation

We investigate the effect of an external periodic modulation on the one-dimensional (1D) Bose–Einstein condensate with harmonic trapping potential. By numerically solving the Gross–Pitaevskii equation with symplectic algorithm, the nonlinear resonance phenomenon is shown and the corresponding Fourier spectrum is given. The autoresonance phenomenon is also presented under almost periodic external modulation, and it shows that the condensate eventually evolves into quasi-periodic oscillation.