Quantum Analog Simulation of the (Anti-)Jaynes–Cummings Hamiltonian in the Ultrastrong-Coupling Regime

The (Anti-)Jaynes-Cummings (JC/AJC) Hamiltonian is a fundamental model describing light-matter interactions. Although the ultrastrong-coupling (USC) regime of the Rabi model has been extensively explored through quantum simulation, experimental investigations specifically addressing the JC/AJC Hamiltonian in this regime remain limited. Here, we propose a theoretical method for realizing an effective JC/AJC Hamiltonian in the USC regime using quantum analog simulation. A potential implementation within a circuit quantum electrodynamics (cQED) platform is investigated, discussing its practical pathways and limitations. Moreover, by leveraging the established mapping between the JC/AJC Hamiltonian and the Dirac oscillator, this work provides a framework for the experimental realization of a quantum analog simulator for a fundamental relativistic system.