Joseph studied the Fermi-Hubbard model, a theoretical model that captures the insulating and conducting phases of high temperature superconducting materials, where he characterized novel quantum phases and dynamics realized on cutting-edge quantum simulation platforms. By correlating maps of the local density of states, the local magnetization, and the local bond conductivity, he found a collapse of the Mott gap toward a V-shape pseudo-gapped density of states that occurs concomitantly with the decrease of magnetism around the highly disordered sites, while the electronic bond conductivity increases. His results provide one of the first microscopic investigations of dynamical response and how these two phases (correlated metal and Mott insulator) coexist microscopically and lead to an overall macroscopic phase transition. Expanding beyond the ground state properties of interacting matter, he also venture exploring the field of nonequilibrium quantum dynamics that bridges foundational atomic, molecular, and optical and condensed matter models. In relevant works he presented a new framework that connects physical spin-fluctuations, quantum Fisher information, and bipartite entanglement entropy between collective quantum systems.