| Abstract: | Abstract Light states with nontrivial quantum properties are highly sought after both in theory and experiment. In addition to lending themselves well to storing and manipulating quantum information, they turn out to herald quantum correlations in the emitter. Yet, these states of light remain an almost uncharted territory due to the complexity entailed by both observing them in experiment and accurately predicting them in theory. While quantum correlations are an important building block for quantum light states, their buildup is mostly unexplained by existing methods. While one can resort to a perturbative expansion over the light-matter interaction, it will struggle to account for the cascading re-emission and re-absorption of photons involved. Conversely, constraining the mode space will accommodate a non-perturbative treatment, but fail to accurately describe the entanglement of multiple quantum modes with the emitter and with each other. Instead, we adopt a novel multimode non-perturbative approach, which allows us to contain the growth of the photonic Hilbert space. We demonstrate the capability to simulate the behavior of driven systems interacting with multiple quantum electromagnetic modes without reducing the mode space. We consider a system consisting of many (10-500) qubits with no explicit coupling between them, driven classically by a perturbative weak resonant light field, and coupled strongly to a narrow-band waveguide. This setup ensures that, after a photon is emitted by one qubit, it can be reabsorbed by another while retaining entanglement with the original one, giving rise to quantum correlations between the two. The correlated qubits undergo collective transitions, prompting the spontaneous formation of a correlated lightmatter state. The correlations for the many-body state grow over time, which, in turn, gives rise to highly nonclassical photonic emissions.
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