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Acta Physica Sinica

Gazeau-Klauder and Klauder-Perelomov coherert states for the anharmonic oscillator

Yan-Fu Cheng, 中南民族大学物理系,武汉　430074

Published Jan 1, 2004• 0 citations
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Abstract

Using the Kinani-Daoud method we have constructed the Gazeau-Klauder(GK) and KlauderPerelomov(KP) coherent states for the anharmonic oscillator. It is shown that the two types of coherent states have totally different forms in their expressions. We have also discussed the resolution of unity of the two coherent states and the Hilbert space of each state. The study of Mandel Q pa rameter of the states shows that GK coherent state coincides with the sub-Poissonian and KP coherent state coincides with the super-Poissonian statistical distributions.

DOI
10.7498/aps.53.3657

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Using the Kinani-Daoud method we have constructed the Gazeau-Klauder(GK) and KlauderPerelomov(KP) coherent states for the anharmonic oscillator. It is shown that the two types of coherent states have totally different forms in their expressions. We have also discussed the resolution of unity of the two coherent states and the Hilbert space of each state. The study of Mandel Q pa rameter of the states shows that GK coherent state coincides with the sub-Poissonian and KP coherent state coincides with the super-Poissonian statistical distributions.
Firstly, the solvability of some quantum models like Eckart and Rosen–Morse II are explained on the basis of the shape invariance theory. Then, two generalized types of the Klauder–Perelomov and Gazeau–Klauder coherent states are calculated for the models. By means of calculating the Mandel parameter, it is shown that the weight distribution function of the first type coherent states obeys the Poissonian and super-Poissonian statistics, however, the weight distribution function of the second type coherent states obeys the Poissonian and sub-Poissonian statistics.
A one-dimensional nonlinear harmonic oscillator is studied in the context of generalized coherent states. We develop a perturbative framework to compute the eigenvalues and eigenstates for the quantum nonlinear oscillator and construct the generalized coherent states based on Gazeau-Klauder formalism. We analyze their statistical properties by means of Mandel parameter and second order correlation function. Our analysis reveals that the constructed coherent states exhibit super-Poissonian statistics. Moreover, it is shown that the coherent states mimic the phenomena of quantum revivals and fractional revivals during their time evolution. The validity of our results has been discussed in terms of various parametric bounds imposed by our computational scheme.
Generalized coherent states based on Gazeau-Klauder formalism are developed for one-dimensional power-law potentials and their quantum statistical characteristics, together with generalized Heisenberg algebra coherent states, are reported. We show that these states exhibit super-Poissonian, Poissonian, or sub-Poissonian distributions as a function of the power-law exponent. The analytical results are supported by numerical calculations. In addition, we explain possible sources of errors in numerical analysis.
In the last decades, much attention has been paid to the excitation on coherent states, especially for coherent states of the harmonic oscillator ([1] and references therein). But an interesting anharmonic oscillator with many potential applications is also the pseudoharmonic oscillator (PHO). So, in the present paper we have defined the excitation on the Klauder‐Perelomov coherent states (E‐KP‐CSs) for the PHO. These states are obtained by repeatedly operating the raising operator K+ on a usual Klauder‐Perelomov coherent state (KP‐CS) of the PHO [2]. We have verified that really, the E‐KP‐CSs fulfill all the properties of the coherent states, as stated by Klauder [3]. We have examined the nonclassical properties of the E‐KP‐CSs, by using the density matrix formalism and examining the dependence of the Mandel parameter Qz,k;m(|z|2) on the |z|2 and on the m. It seems that these states can be used in optical communication field and in the physics of quantum information, as signal beams, due to the fact that in these fields the nonclassicality plays an important role.