Reconstruction of the phase of matter-wave fields using a momentum-resolved cross-correlation technique

We investigate the potential of the so-called cross-correlation frequency-resolved optical gating (XFROG) technique originally developed for ultrashort laser pulses for the recovery of the amplitude and phase of the condensate wave function of a Bose-Einstein condensate. Key features of the XFROG method are its high resolution, versatility, and stability against noise and some sources of systematic errors. After showing how an analog of XFROG can be realized for Bose-Einstein condensates, we illustrate its effectiveness in determining the amplitude and phase of the wave function of a vortex state. The impact of a reduction of the number of measurements and of typical sources of noise on the field reconstruction are also analyzed.