Abstract
We propose a fast scheme to generate Schr\"odinger cat states in a superconducting resonator using a continuously driven qubit without resorting to the dispersive regime, two-photon drives, or engineered two-photon dissipation. We provide analysis for when the qubit is on and off resonance from the drive. We extend our analysis to account for a third level in a weakly-anharmonic qutrit. We also discuss the case of a strongly-anharmonic qutrit. Throughout the paper, we corroborate our analytical results with numerical simulations in the presence of energy relaxation and dephasing of the qubit and resonator using realistic experimental parameters.