We will build a superconducting circuit to simulate light–matter interaction beyond the strong-coupling limit: a fluxonium qubit coupled to a microwave resonator, with a coupling tuned in situ from zero up to the deep-strong regime, where it exceeds the bare frequencies of both. In this regime, the ground state becomes an entangled atom–field superposition, a Schrödinger cat, and the Dicke and spin-boson models predict quantum phase transitions driven by the interaction itself. Measuring these states remains an open challenge: once atom and photon hybridize, one can no longer read them out separately. Our approach relies on a new coupler, a Wheatstone bridge of Josephson inductances. When the bridge is balanced, the coupling vanishes by symmetry; a magnetic flux unbalances it and tunes the coupling in magnitude and sign. Switching the coupling off within a nanosecond projects the hybridized state onto the uncoupled basis, where standard readout applies. The student will first design the device using circuit quantization and numerical simulations, and develop superconducting air bridges in the ENS clean room. Depending on progress, the student will then fabricate the full circuit and perform its first spectroscopy at 10 mK. The internship can be continued as a PhD.