This article is cited in
3 papers
$q$-Deformed Barut–Girardello $su(1,1)$ coherent states and Schrödinger cat states
Yuefeng Zhao,
Yan Zeng,
Honggang Liu,
Qi Song,
Gangcheng. Wang,
Kang Xue Department of Physics, Northeast Normal University,
Changchun, Republic of China
Abstract:
We define Schrödinger cat states as superpositions of
$q$-deformed
Barut–Girardello
$su(1,1)$ coherent states with an adjustable angle
$\varphi$
in a
$q$-deformed Fock space. We study the statistical properties of the
$q$-deformed Barut–Girardello
$su(1,1)$ coherent states and Schrödinger
cat states. The statistical properties of photons are always sub-Poissonian
for
$q$-deformed Barut–Girardello
$su(1,1)$ coherent states. For
Schrödinger cat states in the cases
$\varphi=0,\pi/2,\pi$, the statistical
properties of photons are always sub-Poissonian if
$\varphi=\pi/2$, and the other cases are hard to determine because they depend on the parameters
$q$
and
$k$. Moreover, we find some interesting properties of Schrödinger cat
states in the limit
$|z|\to0$, where
$z$ is the parameter of those states.
We also derive that the statistical properties of photons are sub-Poissonian
in the undeformed case where
$\pi/2\le\varphi\le3\pi/2$.
Keywords:
$q$-deformed Barut–Girardello algebra, $su(1,1)$ coherent state, $q$-deformed cat state. Received: 31.03.2016
DOI:
10.4213/tmf9200