Generalized Husimi operator as the rotated and squeezed coherent state projector and its application

• Published in: Journal of physics. B, Atomic, molecular, and optical physics Vol. 46; no. 4; pp. 45501 - 1-4
• Main Authors: Xu, Ye-jun, Wang, Xian-cai, Gui, Chuan-you, Zhu, Zheng-fang
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 28.02.2013; Institute of Physics
• Subjects: Atom, molecule and ion trapping and colling methods; Atomic and molecular physics; Classical and quantum physics: mechanics and fields; Coherence; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Husimi operator; Mechanical control of atoms, molecules and ions; Nonclassical field states; squeezed, antibunched and sub-poissonian states; operational definitions of the phase of the field; phase measurements; Operators; Optics; Physics; Projectors; Quantum mechanics; Quantum optics; quantum state reconstruction; Quantum optics; Trapped ions; Squeezed states; Coherent states; Harmonic potential
• ISSN: 0953-4075; 1361-6455
• DOI: 10.1088/0953-4075/46/4/045501

We propose a so-called generalized Husimi operator gh(x, p, κ, θ) corresponding to the generalized Husimi function and prove gh(x, p, κ, θ) = |x, p, κ, θ〉〈x, p, κ, θ|, i.e. gh(x, p, κ, θ) is actually a pure state projector. Further, |x, p, κ, θ〉 turns out to be a rotated and squeezed coherent state . As an application, we propose a measured scheme on the generalized Husimi function in the context of a single trapped ion.