  Disorder in one-dimensional (1D) many-body systems emerges abundant phases
such as many-body localization (MBL), and thermalization. However, it remains
unclear regarding their existence and behavior within hybrid quantum systems.
Here, based on a simple bosonic-spin hybrid model, as known as the
Jaynes-Cummings-Hubbard (JCH) array, we investigate the effect of disorder
comparing to the phenomena in the clean system with the variation of
atom-photon coupling strength. By using the level-spacing ratio, entanglement
entropy, and the properties of observable diagonal and off-diagonal matrix
elements, we find that strong disorder results in the appearance of MBL phase
in the JCH model that strongly violate eigenstate thermalization hypothesis
(ETH), while a conditional prethermal behavior can exist in weak disorder or
weak coupling regime. The conditional prethermal dynamics is based on the
choice of initial product states. This work systematically reveals abundant
many-body phases in the 1D JCH model and clarifies the discrepancies in the
thermalization properties of systems with and without disorder.
