We study the bound and antibound states of two excitons in a GaAs single quantum well by two-dimensional coherent spectroscopy. We also propose a method to directly observe the amplitude and phase (real and imaginary parts) of optical fields by using a heterodyne interference technique and through synchronized detection of the interference signals. In this scheme, the mechanical fluctuation of an unstabilized interferometer does not affect the measurement. In addition, the amplitude and phase of the optical fields, resulting from the coherent interactions between light and matter, are directly obtained by comparing a reference heterodyne beating signal by using a two-phase lock-in amplifier. By using this method, the bound and antibound states of two excitons are observed. It is expected that the excitons are localized to the quantum islands and the lateral confinement induces the large repulsive energy between the two excitons.