By analytically solving the quantum Rabi model, we investigate the photonic properties of its ground eigenstate. In particular, we find that in the deep strong coupling regime, where the coupling strength
g exceeds the mode frequency
ω, the photonic state is effectively squeezed in one of its quadratures. The squeezing reaches its maximum at the curve corresponding to the quantum phase transition of the quantum Rabi system, and decreases rapidly on both sides of the phase transition. Notably, for
g/ω≈3, which is experimentally testable in existing trapped-ion platforms, the achievable squeezing parameter can reach approximately
r≈0.8. Intriguingly, the photonic state is squeezed while its number distribution follows a super-Poissonian distribution, with the largest deviation from Poissonian behavior occurring at the phase transition between the normal and superradiant phases. In other words, the ground state of the quantum Rabi model contains super-Poissonian quantum squeezed photons.
Accessing chaos in the quantum Rabi model (QRM) usually requires operating far from resonance, combined with ultra- or deep-strong light-matter coupling.
This makes direct experiments challenging.
In this manuscript, we propose a solution to this challenge by employing an anti-squeezing transformation to the bosonic field.
Specifically, we demonstrate that this transformation maps a weakly coupled, two-photon driven Jaynes-Cummings model (JCM) to an effective deep-strong-coupling QRM in the squeezed-light frame.
Using out-of-time-order correlator, Husimi distribution, and linear entanglement entropy, we numerically probe chaos in this coupling-enhanced platform and observe the similar chaotic phenomena as in the ideal QRM.
We also find the coupling-enhanced model can drive the system deeper into the chaotic regime.
This establishes coupling-enhanced method as a practical approach to study QRM chaos without requiring intrinsic ultra-strong coupling.
Strong light-matter coupling enables hybrid states in which photonic and electronic degrees of freedom become correlated even in the ground state. While many-body effects in long-range dispersion interactions are known to reshape electronic properties under such conditions, their impact on quantum-optical observables remains largely unexplored. Here, we address this problem using quantum electrodynamical density-functional theory (QEDFT) combined with the recently developed photon-many-body dispersion (pMBD) functional, which can capture higher-order electron-photon correlations and multi-photon processes. We compute ground-state photonic observables including photon number fluctuations, second-order correlations, and quadrature variances, and find squeezing and super-Poissonian photon statistics emerging from light-matter interactions in the strong coupling regime. Our results demonstrate that capturing the full hierarchy of many-body, electron-photon and multi-photon correlations is essential for a consistent description of quantum-optical properties in strongly coupled molecular systems, establishing QEDFT as a first-principles framework for predicting nonclassical photonic features in the ground state of complex systems.