Light-matter interaction between an atom and an electromagnetic resonator is ubiquitous in quantum technologies. Although linear light-matter coupling
gσ^x(a^+a^†) can reach the ultrastrong regime g/ω > 10−1, nonlinear light-matter coupling
2χσ^za^†a^ is typically perturbative and limited to χ/ω < 10−2. Nonlinear coupling has the advantage of commuting with the atomic
σ^z and photonic
a^†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 (
χa^†a^b^†b^ ) and χ/2π = 580.3 ± 0.4 MHz matter-matter nonlinear coupling (
4χσ^z,aσ^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. Nonlinear light-matter coupling has applications in quantum technologies, for instance in quantum-non-demolition measurements, but its strength is typically limited. Here the authors demonstrate near-ultrastrong nonlinear light-matter coupling in a superconducting circuit with two transmons and a quarton coupler.
It is well known that superconducting waveguides strongly attenuate the propagation of electromagnetic waves with frequencies beyond the superconducting gap. In circuit QED, the interaction between non-linear charge qubits and superconducting resonators invariably involves the qubit coupling to a large set of resonator modes. So far, strong dispersion effects near and beyond the superconducting-gap have been ignored in quantization models. Rather, it is assumed that the superconducting resonator behaves ideally across the large frequency intervals. We present a quantization approach which includes the superconducting frequency-dependent surface impedance and demonstrate that superconducting dispersion plays a role in determining the effective light-matter interaction cut-off.