Strongly Driven Two-Photon Qubit-Resonator Interactions: Nonclassical States, Qubit Readout, and More

Nonlinear interactions are a fundamental tool for creating and manipulating useful quantum-mechanical phenomena. There is a recent surge of interest in a qubit interacting with a resonator through multi-photon processes for various purposes, such as creating nonclassical states in the resonator or using the resonator as a coupler between multiple qubits. In the context of nonlinear qubit-resonator interactions in circuit QED, we discuss a driven qubit coupled to a resonator via a two-photon interaction. We explore the strong driving regime of this system to generate a superposition of the qubit ground and excited states entangled with two oppositely squeezed states. In this entangled state, measuring the qubit leaves the resonator in a superposition of oppositely squeezed states. This, incidentally, facilitates the encoding of a qubit state into the resonator using squeezed states, akin to how qubit states are encoded using coherent states (bosonic cat codes). Alternatively, measuring the resonator allows us to perform a QND measurement of the qubit state. This protocol yields a resonator photon number that grows in a hyperbolic-quadratic manner in time. We also showcase the dynamics in the case of a weaker drive. Lastly, we demonstrate the robustness of this method in the presence of qubit and resonator decoherence.