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Acta Physica Sinica

ORTHONORMALIZED EIGENSTATES OF OPERATOR αN AND THEIR PROPERTIES

PENG SHI-AN, Guo Guang-Can, (1)河北师范学院物理系,石家庄,050091; (2)中国科学技术大学物理系,合肥,230026

Published Jan 1, 1990• 6 citations
Publisher

Abstract

In this paper, a general method for constructing orthonormalized eigenstates of operator αN is presented. The emphasis is put on study of mathematical structure and quantum statistical properties in the case N=3. It is found that all the orthonorma-lizetl eigenstates have nonclassical effects and they form a nonclassical complete representation.

DOI
10.7498/aps.39.51

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In this paper, a general method for constructing orthonormalized eigenstates of operator αN is presented. The emphasis is put on study of mathematical structure and quantum statistical properties in the case N=3. It is found that all the orthonorma-lizetl eigenstates have nonclassical effects and they form a nonclassical complete representation.
We have studied the orthonormalized eigenstates of the higher powers ak{\mathit{a}}^{\mathit{k}}ak (k\ensuremath{\ge}3) of the annihilation operator a and their properties. Our conclusions are as follows: (1) The orthonormalized eigenstates of ak{\mathit{a}}^{\mathit{k}}ak construct a complete representation with respect to \ensuremath{\alpha}. (2) None of the orthonormalized eigenstates of ak{\mathit{a}}^{\mathit{k}}ak shows the squeezing effect in the usual sense. (3) All of the eigenstates of ak{\mathit{a}}^{\mathit{k}}ak show the antibunching effect.
Quantum statistical properties of orthonormalized eigenstates of the operator (â f (n^\hat nn^))k
The completeness of the k orthonormalized eigenstates of the operator (â f ( )) k ( k ⩾3) is investigated. We introduce a new kind of higher-order squeezing and an antibunching. The properties of the M th-order squeezing and the antibunching effect of the k states are studied. The result shows that these states may form a complete Hilbert space, and the M th-order ( M = ( n + 1/2) k ; n = 0,1,...) squeezing effects exist in all of the k states when k is even. There is an antibunching effect in all of the states. An alternative method for constructing the k states is proposed, and the result shows that all of them can be generated by linear superposition of the time-dependent nonlinear coherent states at different instants.