Investigating and analysis of the properties of coherent states of a deformed nonlinear harmonic oscillator

• Published in: Iranian Journal of Physics Research Vol. 23; no. 2; pp. 405 - 417
• Main Authors: Mohsen Daeimohammad, Mohammad Nili Ahmadabadi
• Format: Journal Article
• Language: English
• Published: Isfahan University of Technology 01-09-2023
• Subjects: coherent states; deformed nonlinear harmonic oscillator; mandel parameter; super-poissonian and sub-poissonian statistical distributions; the bunching and antibunching effects
• ISSN: 1682-6957; 2345-3664
• DOI: 10.47176/ijpr.23.2.61705

In this research, we study the coherent states of a deformed nonlinear harmonic oscillator. We use the perturbation theory to compute eigenstates and eigen-values ​​for a deformed nonlinear harmonic oscillator and then define the generalized coherent states based on the Gazeau-Klauder formulation. Then, using the Mandel parameter and the second-order correlation function, we will investigate the statistical properties of the system. The analysis shows that the coherent states for a deformed and non-deformed nonlinear harmonic oscillator follows the sub-Poissonian and super-Poissonian statistics, and exhibits the antibunching and bunching effects, respectively. In addition, we show that the anti-correlation function for a deformed nonlinear oscillator is strongly fluctuating and irregular. Also, the anti-correlation function of a non-deformed nonlinear harmonic oscillator shows the phenomena of collapse and revival of fractional revelations. We also examine the limits of different parameters so that the obtained results are valid.