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TMF, 2017, Volume 193, Number 3, Pages 505–514 (Mi tmf9200)  

$q$-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.

Funding Agency Grant Number
National Natural Science Foundation of China 11405026
11175043
Department of Education of Jilin Province 20150520083JH
Fundamental Research Funds for the Central Universities of China 14QNJJ008
This research was supported by the NSF of China (Grant Nos. 11405026 and 11175043), the Plan for Scientific and Technological Development of Jilin Province (Grant No. 20150520083JH), and the Fundamental Research Funds for the Central Universities (Grant No. 14QNJJ008).


DOI: https://doi.org/10.4213/tmf9200

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English version:
Theoretical and Mathematical Physics, 2017, 193:3, 1844–1852

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Received: 31.03.2016

Citation: Yuefeng Zhao, Yan Zeng, Honggang Liu, Qi Song, Gangcheng. Wang, Kang Xue, “$q$-Deformed Barut–Girardello $su(1,1)$ coherent states and Schrödinger cat states”, TMF, 193:3 (2017), 505–514; Theoret. and Math. Phys., 193:3 (2017), 1844–1852

Citation in format AMSBIB
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