Observing phase jumps of solitons in Bose-Einstein condensates

The phase difference of the macroscopic wave function is a unique structure of the soliton in an atomic Bose--Einstein condensate (BEC). However, experiments on ultracold atoms so far have observed the valley of the density profile to study the dynamics of solitons. We propose a method to observe the phase difference of a soliton in a BEC by using an interference technique with Raman and rf pulses. We introduce a phase jump factor, which is an indicator to measure the phase difference between two points. It is demonstrated by using the projected Gross--Pitaevskii equation that an interference density ratio, the density ratio of two-component BECs after the Raman and rf pulses, reproduces the phase jump factor well. This technique will become an alternative method to study the decay and breakdown of a phase imprinted soliton in atomic BECs.