We investigate the simulation of Jahn-Teller models with two non-degenerate
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 isolating the effective single frequency and pure
two-frequency effects in the spectral response of Jahn-Teller systems.Comment: 8 pages, 4 figures, figures revise
