Geodesic
$q$-Deformed Barut--Girardello $su(1,1)$ coherent states and Schr\"odinger cat states
Teoretičeskaâ i matematičeskaâ fizika, Tome 193 (2017) no. 3, pp. 505-514

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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. 
@article{TMF_2017_193_3_a9,
     author = {Yuefeng Zhao and Yan Zeng and Honggang Liu and Qi Song and Gangcheng. Wang and Kang Xue},
     title = {$q${-Deformed} {Barut--Girardello} $su(1,1)$ coherent states and {Schr\"odinger} cat states},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {505--514},
     publisher = {mathdoc},
     volume = {193},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2017_193_3_a9/}
}
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Yuefeng Zhao; Yan Zeng; Honggang Liu; Qi Song; Gangcheng. Wang; Kang Xue. $q$-Deformed Barut--Girardello $su(1,1)$ coherent states and Schr\"odinger cat states. Teoretičeskaâ i matematičeskaâ fizika, Tome 193 (2017) no. 3, pp. 505-514. http://geodesic.mathdoc.fr/item/TMF_2017_193_3_a9/