×

Squeezed variances of smeared boson fields. (English) Zbl 0891.46041

Summary: Our previous investigations on squeezing Bogoliubov transformations in the smeared field formalism are continued. After a short introduction into the usual form of squeezing operations in quantum optics the rigorous version is formulated first in terms of certain quasifree automorphisms on the \(C^*\)-Weyl algebra over a testfunction space of arbitrary dimension, and then as their dual transformations on the abstract state space. For selected classes of states the fluctuations are determined before and after such a transformation, and a general definition of a squeezed state is proposed. Especially for quasifree, classical, and coherent photon states detailed estimations for their transformed fluctuations are elaborated using a spectral theory of the general squeezing operator. Explicit criteria for non-classicality are specified and applied to squeezed white noise and other Gaussian states. It is shown, that strong squeezing of one-mode Gaussian states leads to mixed non-classical coherent states.

MSC:

46L60 Applications of selfadjoint operator algebras to physics
81V80 Quantum optics
46N50 Applications of functional analysis in quantum physics
81R30 Coherent states
PDFBibTeX XMLCite