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Localization of states, Bloch wave and quantum phase transitions in SUSY deformed potentials in non-Hermitian optical systems

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.