Geometric Phase of Soliton Induced by Chirp Modulation

Abstract It has been shown that the profile variation of wavepackets can induce additional geometric phases in addition to the ones induced by the classical action induced by the wavepackets’ orbital motion, within the framework of squeezed states. In this work, we employ the Lagrangian variational method to investigate the geometric phase of bright solitons in a harmonic potential under both nonlinearity and chirp modulations. It is shown that the geometric phase consists of two distinct parts during cyclic evolution: one originates from the classical action induced by orbital motion of the soliton, and the other is induced by the variation of the soliton’s profile. We demonstrate via numerical simulation and analytical analysis that the variation of the soliton profile induced by nonlinear modulation does not give rise to a geometric phase, whereas chirp modulation does. Furthermore, a correspondence exists between the magnitude of the initial chirp and the strength of the harmonic potential. Our results offer a feasible approach to observe the geometric phase of a soliton in Bose-Einstein condensates.