Rabi model with diamagnetic term and its waveguide realization

We explicitly show that a transformation based on the squeeze operator enables an exact mapping – without any approximation – of the light–matter interaction Hamiltonian, including the $A^2$ (diamagnetic) term, to the standard Rabi model Hamiltonian. This result underscores the novelty of our approach, as it establishes a rigorous equivalence even in the presence of terms typically excluded in conventional derivations. Additionally, we propose partner waveguide arrays that simulate both the full Hamiltonian with the diamagnetic term and the conventional Rabi Hamiltonian.