Radiation-pressure interactions between harmonic oscillators have enabled exquisite measurement precision and control, made possible by using strong sideband drives, enhancing the coupling rate while also linearizing the interaction. In this Letter, we demonstrate a strong intrinsic longitudinal coupling, a circuit quantum electrodynamics analog of the radiation-pressure interaction, between a transmon qubit and a linear microwave resonator. A red-detuned sideband drive results in an on-demand Jaynes-Cummings interaction with a high on-off ratio. We measure a longitudinal coupling rate an order of magnitude larger than all decay rates, placing the device in the strong coupling regime. The intrinsic longitudinal interaction demonstrated here will enable the development of high-connectivity quantum information processing hardware and the exploration of the gravitational decoherence of quantum objects.

Microwave driving is a ubiquitous technique for superconducting qubits, but the dressed states description based on the conventionally used perturbation theory cannot fully capture the dynamics in the strong driving limit. Comprehensive studies beyond these approximations applicable to transmon-based circuit quantum electrodynamics (QED) systems are unfortunately rare, as the relevant works have been mainly limited to single-mode or two-state systems. In this work, we investigate a microwave-dressed transmon coupled to a single quantized mode over a wide range of driving parameters. We reveal that the interaction between the transmon and resonator as well as the properties of each mode is significantly renormalized in the strong driving limit. Unlike previous theoretical works, we establish a nonrecursive and non-Floquet theory beyond the perturbative regimes, which excellently quantifies the experiments. This work expands our fundamental understanding of dressed cavity QED-like systems beyond the conventional approximations. Our work will also contribute to fast quantum gate implementation, qubit parameter engineering, and fundamental studies on driven nonlinear systems.