Adiabatic Evolution and Fock-state Mapping Across the Phase Boundary in a Quantum Rabi Dimer

The quantum Rabi dimer serves as a minimal model for exploring light–matter interactions and critical phenomena in coupled cavity-QED systems. We investigate the adiabatic evolution of this system, beginning from the ground state of an initially uncoupled dimer. Using a QuTiP-based eigensolver, we numerically compute the energy spectrum and Fock-state distributions of the low-lying eigenstates. We further evaluate the fidelity susceptibility across parameter space, which exhibits clear signatures of a phase transition. The adiabatic trajectories reveal distinct features as the system crosses the phase boundary. These results pave the route to understanding the critical behavior in coupled cavity-QED architectures.