Single- and Two-Mode Squeezing by Modulated Coupling to a Rabi Driven Qubit

Advanced bosonic quantum computing architectures demand nonlocal Gaussian operations such as two-mode squeezing to unlock universal control, enable entanglement generation, and implement logical operations across distributed modes. This work presents a novel method for generating conditional squeezing using a Rabi-driven qubit dispersively coupled to one or two harmonic oscillators. A proof that this enables universal control over bosonic modes is provided, expanding the toolkit for continuous-variable quantum information processing. Using modulated Jaynes-Cummings interactions in circuit QED, the simulation predicts intra-cavity squeezing of 13dB (single-mode), 4dB (superimposed single-mode), and 12dB (two-mode), with the latter two yet to be demonstrated experimentally. These results establish a new paradigm for qubit-conditioned control of photonic states, with applications to quantum sensing and continuous-variable computation on readily available systems.