arXiv2024
The interaction between an atom and an electromagnetic mode of a resonator is of both fundamental interest and is ubiquitous in quantum technologies. Most prior work studies a linear light-matter coupling of the form $g \widehatσ_x (\widehat{a} + \widehat{a}^\dagger)$, where $g$ measured relative to photonic ($ω_a$) and atomic ($ω_b$) mode frequencies can reach the ultrastrong regime ($g/ω_{a}\!>\!10^{-1}$). In contrast, a nonlinear light-matter coupling of the form $\fracχ{2} \widehatσ_z \widehat{a}^\dagger \widehat{a}$ has the advantage of commuting with the atomic $\widehatσ_z$ and photonic $\widehat{a}^\dagger\widehat{a}$ Hamiltonian, allowing for fundamental operations such as quantum-non-demolition measurement. However, due to the perturbative nature of nonlinear coupling, the state-of-the-art $χ/\text{max}(ω_a, ω_b)$ is limited to $\!<\!10^{-2}$. Here, we use a superconducting circuit architecture featuring a quarton coupler to experimentally demonstrate, for the first time, a near-ultrastrong $χ/\text{max}(ω_a, ω_b)= (4.852\pm0.006)\times10^{-2}$ nonlinear coupling of a superconducting artificial atom and a nearly-linear resonator. We also show signatures of light-light nonlinear coupling ($χ\widehat{a}^\dagger\widehat{a}\widehat{b}^\dagger\widehat{b}$), and $χ/2π= 580.3 \pm 0.4 $ MHz matter-matter nonlinear coupling ($\fracχ{4}\widehatσ_{z,a}\widehatσ_{z,b}$) which represents 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 applications such as orders of magnitude faster qubit readout and gates.