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Shock waves emerge in various fields and trigger effects like rogue waves, super-continuum generation and emission of resonant radiation. Despite shock waves ubiquity, their effect on the coherence properties is barely understood. Among the open problems, the quantum features of shock waves are particularly intriguing for the possibility of generating non-classical states by highly nonlinear regimes. In this manuscript, we theoretically predict classical squeezing of light during shock formation. By using techniques of rigged Hilbert space quantum mechanics, we show that a coherent state develops squeezing which stops in proximity of the shock point. Our analysis holds true for temporal and spatial shock waves in highly nonlocal regime. These results open a new scenario in shock phenomena and link nonlinear propagation in extreme regimes with quantum optics and related applications.

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