Fischer F, Burgarth D, Lonigro D (2026)
Publication Language: English
Publication Type: Journal article
Publication year: 2026
Book Volume: 59
Article Number: 255203
Journal Issue: 25
Higher-order squeezing captures non-Gaussian features of quantum light by probing moments of the field beyond the variance, and is associated with operators involving nonlinear combinations of creation and annihilation operators. Here we study a class of operators of the form (Formula presented) (Formula presented), which arise naturally in the analysis of higher-order quantum fluctuations. The operators are defined on the linear span of Fock states. We show that the essential self-adjointness of these operators depends on the asymptotics of the real-valued function (Formula presented) (Formula presented) at infinity. In particular, pure higher-order squeezing operators ( (Formula presented) (Formula presented), (Formula presented) (Formula presented), and (Formula presented) (Formula presented) ) are not essentially self-adjoint, but adding a properly chosen term (Formula presented) (Formula presented), like a Kerr term, can have a regularizing effect and restore essential self-adjointness. In the non-self-adjoint regime, we compute the deficiency indices and classify all self-adjoint extensions. Our results provide a rigorous operator-theoretic foundation for modeling and interpreting higher-order squeezing in quantum optics, and reveal interesting connections with the Birkhoff–Trjitzinsky theory of asymptotic expansions for recurrence relations.
APA:
Fischer, F., Burgarth, D., & Lonigro, D. (2026). Self-adjoint realizations of higher-order squeezing operators. Journal of Physics A: Mathematical and Theoretical, 59(25). https://doi.org/10.1088/1751-8121/ae7acb
MLA:
Fischer, Felix, Daniel Burgarth, and Davide Lonigro. "Self-adjoint realizations of higher-order squeezing operators." Journal of Physics A: Mathematical and Theoretical 59.25 (2026).
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