  For the first time, we have observed the annihilation of multiple eigenstates
of the parent potentials and redistribution of the energy in the deformed
potentials in the system with spontaneously breaking of parity-time symmetry
while preserving the SUSY of the system. We have observed that the deformation
of the potentials is sensitive to initial conditions. This first experimental
observation enables the localization of eigenspectra in lateral space
(so-called time) and the localization of eigenstates in longitudinal space in
the deformed potentials by experimentally applying the SUSY higher-order
transformations on tilted and disordered parent potentials, respectively. The
former shows a decrease in the slope of the profile of eigenspectrum (bands)
due to the localization in lateral space, while the latter shows an increase in
the slope due to localization in longitudinal space. This allows the formation
of deterministic bandgaps and Bloch waves while retaining the SUSY. In this
configuration, the phase transition emerges naturally in the SUSY deformed
potentials, which are revealed as the quantum Zeno effect and a peculiar
Anderson localization, respectively. The Anderson localization shows the
features of effective amplification and quantum Anti-Zeno effect. The
experimental results are in full agreement with the theory of SUSY deformed
potentials of higher-order transformations. Besides enhancing the understanding
of nature, our results can also provide an experimental platform to originate
new classes of effective and synthetic materials, and are also significantly
important for unifying the interaction dynamics of condensed matter and
photonic systems, and the implementation of universal quantum computation.
