We consider non-Gaussianity in open quantum systems by finding and characterizing exact ground states of nonlinearly coupled anharmonic oscillators. Tracing out the hidden sector oscillator, we find that the non-Gaussianity of the observable mode may be either enhanced or suppressed by nonlinear coupling to a hidden, non-Gaussian mode. We use a known family of quasiexactly solvable anharmonic oscillators to construct exact, rather than perturbative, ground state solutions. These include states of extreme classical non-Gaussianity and strong quantum non-Gaussianity (infinite stellar rank). The calculation generalizes the classic, bilinearly coupled oscillator example, used for the black hole area law, to non-Gaussian quantum states whose entanglement properties are more complex. If the visible sector field is nondynamical and plays the role of a coupling parameter in the late universe, our results suggest novel statistics for disordered, or space-time dependent, couplings. This class of constructions allows useful exploration of strongly non-Gaussian states and fields, including a means to characterize the robustness of non-Gaussianity to interactions with environmental modes.

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• Cosmological parameters
• Open quantum systems & decoherence
• Quantum correlations in quantum information
• Quantum cosmology