| Summary: | 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 [formula], where 𝑔 measured relative to photonic (𝜔ₐ) and atomic (𝜔 subscript 𝑏) mode frequencies can reach the ultrastrong regime [formula]. In contrast, a nonlinear light-matter coupling of the form [formula] has the advantage of commuting with the atomic [formula] and photonic â superscript † 𝑎 Hamiltonian, allowing for fundamental operations such as quantum-non-demolition (QND) measurement. However, due to the perturbative nature of nonlinear coupling, the state-of-the-art 𝜒/max(𝜔𝑎, 𝜔𝑏) is limited to < 10⁻². In this thesis, we develop the theory of quarton couplers and experimentally demonstrate, for the first time, a near-ultrastrong 𝜒/max(𝜔ₐ, 𝜔 subscript 𝑏) = (4.852 ± 0.006) × 10⁻² nonlinear coupling of a superconducting artificial atom and a nearly-linear resonator. We also show signatures of light-light nonlinear coupling [formula], and 𝜒/2𝜋 = 580.3 ± 0.4 MHz matter-matter nonlinear coupling [formula] which represents the largest reported 𝑍𝑍 interaction between two coherent qubits. Finally, we present a new qubit readout scheme that uses the quarton coupler to enable simulated performance of 5 ns readout time with greater than 99% readout and QND fidelity. Our work reveals a new path for order-of-magnitude improvements of fundamental superconducting qubit operations by engineering nonlinear light-matter couplings in parameter regimes unreachable by existing designs.
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