  In many unconventional superconductors, the pairing of electrons is driven by
the repulsive interaction, which leads to the sign reversal of superconducting
gaps along the Fermi surfaces (FS) or between them. However, to measure this
sign change is not easy and straightforward. It is known that, in
superconductors with sign reversal gaps, non-magnetic impurities can break
Cooper pairs leading to the quasiparticle density of states in the
superconducting state. The standing waves of these quasiparticles will
interfere each other leading to the quasiparticle interference (QPI) pattern
which carries the phase message reflecting also the superconducting gap
structure. Based on the recently proposed defect-bound-state QPI technique, we
explore the applicability of this technique to a typical iron based
superconductor FeTe$_{0.55}$Se$_{0.45}$ with roughly equivalent gap values on
the electron and hole pockets connected by the wave vector q_2=(0,\pi). It is
found that, on the negative energy side, with the energy slightly below the gap
value, the phase reference quantity $|g(q,-E)|\cos(\theta_{q,+E}-\theta_{q,-E})
becomes negative and the amplitude is strongly enhanced with the scattering
vector q_2, but that corresponding to the scattering between the
electron-electron pockets, namely q_3=(\pi,\pi), keeps all positive. This is
well consistent with the theoretical expectation of the s^+- pairing gap and
thus serves as a direct visualization of the sign reversal gaps. This
experimental observation is also supported by the theoretical calculations with
the Fermi surface structure and s^+- pairing gap.
