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We investigate the simulation of Jahn-Teller models with two nondegenerate vibrational modes using a circuit QED architecture. Typical Jahn-Teller systems are anisotropic and require at least a two-frequency description. The proposed simulator consists of two superconducting lumped-element resonators interacting with a common flux qubit in the ultrastrong coupling regime. We translate the circuit QED model of the system to a two-frequency Jahn-Teller Hamiltonian and calculate its energy eigenvalues and the emission spectrum of the cavities. It is shown that the system can be systematically tuned to an effective single-mode Hamiltonian from the two-mode model by varying the coupling strength between the resonators. The flexibility in manipulating the parameters of the circuit QED simulator permits the isolation of the effective single-frequency and pure two-frequency effects in the spectral response of Jahn-Teller systems.
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