Light-matter interaction between an atom and an electromagnetic resonator is ubiquitous in quantum technologies. Although linear light-matter coupling \(g{\hat{\sigma }}_{x}(\hat{a}+{\hat{a}}^{{{\dagger}} })\) can reach the ultrastrong regime g/ω > 10−1, nonlinear light-matter coupling \(\frac{\chi }{2}{\hat{\sigma }}_{z}{\hat{a}}^{{{\dagger}} }\hat{a}\) is typically perturbative and limited to χ/ω < 10−2. Nonlinear coupling has the advantage of commuting with the atomic \({\hat{\sigma }}_{z}\) and photonic \({\hat{a}}^{{{\dagger}} }\hat{a}\) Hamiltonian, allowing for fundamental operations such as quantum-non-demolition measurement. Here, we use a superconducting circuit to demonstrate the experimental realization of near-ultrastrong χ/ω = (4.852 ± 0.006) × 10−2. We also show signatures of light-light nonlinear coupling ( \(\chi {\hat{a}}^{{{\dagger}} }\hat{a}{\hat{b}}^{{{\dagger}} }\hat{b}\) ) and χ/2π = 580.3 ± 0.4 MHz matter-matter nonlinear coupling ( \(\frac{\chi }{4}{\hat{\sigma }}_{z,a}{\hat{\sigma }}_{z,b}\) ), representing the largest reported ZZ interaction between two coherent qubits. Such advances in the nonlinear coupling strength of light, matter modes enable new physical regimes and could lead to orders of magnitude faster qubit readout and gates.
