Kavli Affiliate: Felix Fischer
| First 5 Authors: Felix Fischer, Felix Fischer, , ,
| Summary:
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 $xi
(a^dag)^ka^l+xi^ast (a^dag)^la^k+f(a^dag a)$, 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 $f(n)$
at infinity. In particular, pure higher-order squeezing operators ($kgeq3$,
$l=0$, and $f(n)=0$) are not essentially self-adjoint, but adding a properly
chosen term $f(a^dag a)$, 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.
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