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Chinese Physics C

Internal Structure and Squeezing Properties of Some Macroscopic Quantum States

Liang Mai

Published Jan 1, 2003• 0 citations

Abstract

Coherent states and the extension to the even and odd coherent states, and further to the eigenstates of the higher power of the annihilation operator are basic and important macroscopic quantum states in quantum field theory. Recently, these investigations have been extended to the aharmonic oscillator and the quantum algebra with q -deformed or qs-deformed commutation relations. In this paper,the orthogonal eigenstates of the higher order of the annihilation operator of the q -deformed aharmonic oscillator are also derived. It is pointed out that these different macroscopic quantum states have similar squeezing properties of higher order amplitude. The reason is found that the orthogonal eigenstates of the higher order of the annihilation operator of the harmonic oscillator, the q -deformed oscillator, the qs -deformed oscillator, the Enharmonic oscillator and the q -deformed anharmonic oscillator all have even and odd structure, which is similar to the simple even and odd coherent states. For other systems like the system with SU(1 ,1) Lie algebra or q -deformed quantum algebra also have such properties.

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Communications in Theoretical Physics•Sep 15, 1997•1 citation

Coherent states and the extension to the even and odd coherent states, and further to the eigenstates of the higher power of the annihilation operator are basic and important macroscopic quantum states in quantum field theory. Recently, these investigations have been extended to the aharmonic oscillator and the quantum algebra with q -deformed or qs-deformed commutation relations. In this paper,the orthogonal eigenstates of the higher order of the annihilation operator of the q -deformed aharmonic oscillator are also derived. It is pointed out that these different macroscopic quantum states have similar squeezing properties of higher order amplitude. The reason is found that the orthogonal eigenstates of the higher order of the annihilation operator of the harmonic oscillator, the q -deformed oscillator, the qs -deformed oscillator, the Enharmonic oscillator and the q -deformed anharmonic oscillator all have even and odd structure, which is similar to the simple even and odd coherent states. For other systems like the system with SU(1 ,1) Lie algebra or q -deformed quantum algebra also have such properties.

The generalized even and odd coherent states of a q-Deformation Non-harmonic Oscillator(E-O q-NHCSs) are constructed,their Higher-Order Squeezing and Antibunching Properties are studied in detail.It is increasing the Squeezing effect in different parameter ranges.With q-deformation increasing,the squeezing effect of E q-NHCSs are weakened and those of O q-NHCSs are enhanced.The E q-NHCSs appear high-order(N≥2) antibunching properties while the O q-NHCSs appear high-order bunching properties in some ranges of the parameter q and r 2 with the q-deformation increasing.Both antibunching effects of E q-NHCSs and bunching effects of O q-NHCSs are enhanced.

In this paper, we use the numerical method to study the influences of and deformations on the quantum statistical properties of even and odd qs-coherent states. It is shown that nonclassical properties of the even and odd qs-coherent states are very different from those of the usual even and odd coherent states. It is found that squeezing and antibunching effect appear for both even and odd qs-coherent states in some range of the parameters , and . The smaller the and are, the larger the difference between the even and odd qs-coherent states and the usual even and odd coherent states is.