Physical Review A

Orthonormalized eigenstates of cubic and higher powers of the annihilation operator

Jinzuo Sun, Ji‐Suo Wang, Chuan‐Kui Wang

Published Sep 1, 1991• 41 citations

Abstract

We have studied the orthonormalized eigenstates of the higher powers ${\mathit{a}}^{\mathit{k}}$ (k\ensuremath{\ge}3) of the annihilation operator a and their properties. Our conclusions are as follows: (1) The orthonormalized eigenstates of ${\mathit{a}}^{\mathit{k}}$ construct a complete representation with respect to \ensuremath{\alpha}. (2) None of the orthonormalized eigenstates of ${\mathit{a}}^{\mathit{k}}$ shows the squeezing effect in the usual sense. (3) All of the eigenstates of ${\mathit{a}}^{\mathit{k}}$ show the antibunching effect.

DOI: 10.1103/physreva.44.3369

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Physical Review A

Orthonormalized eigenstates of cubic and higher powers of the annihilation operator

Jinzuo Sun, Ji‐Suo Wang, Chuan‐Kui Wang

Published Sep 1, 1991• 41 citations

Publisher

Abstract

We have studied the orthonormalized eigenstates of the higher powers

{\mathit{a}}^{\mathit{k}}

(k\ensuremath{\ge}3) of the annihilation operator a and their properties. Our conclusions are as follows: (1) The orthonormalized eigenstates of

{\mathit{a}}^{\mathit{k}}

construct a complete representation with respect to \ensuremath{\alpha}. (2) None of the orthonormalized eigenstates of

{\mathit{a}}^{\mathit{k}}

shows the squeezing effect in the usual sense. (3) All of the eigenstates of

{\mathit{a}}^{\mathit{k}}

show the antibunching effect.

DOI: 10.1103/physreva.44.3369

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Orthonormalized eigenstates of the quantum operator ak and their nonclassical properties

Xiao-Ming Liu, Shun-Jin Wang, ZHANG WEN-ZHONG

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Eigenstates of the Operator $a_{qs}^k$ and Their Antibunching EffectEigenstates of the Operator $a_{qs}^k$ and Their Antibunching Effect

Ji‐Suo Wang, Chang-Yong Sun

Communications in Theoretical PhysicsJun 15, 19970 citations

We have studied the orthonormalized eigenstates of the higher powers

{\mathit{a}}^{\mathit{k}}

(k\ensuremath{\ge}3) of the annihilation operator a and their properties. Our conclusions are as follows: (1) The orthonormalized eigenstates of

{\mathit{a}}^{\mathit{k}}

construct a complete representation with respect to \ensuremath{\alpha}. (2) None of the orthonormalized eigenstates of

{\mathit{a}}^{\mathit{k}}

shows the squeezing effect in the usual sense. (3) All of the eigenstates of

{\mathit{a}}^{\mathit{k}}

show the antibunching effect.

A method for construction of the k orthonormalized quantum eigenstates of the higher powers

{\mathit{a}}^{\mathit{k}}

of the quantum-annihilation operator a is proposed, and their physical meaning is explored. Nonclassical properties of these quantum eigenstates are studied and the main results are as follows: (1) All of the eigenstates can be expressed as a linear superposition of k quantum-coherent states; (2) all of them are generalized quantum-coherent states; (3) for k\ensuremath{\ge}3, they have the Nth-order quantum squeezing for N=mk+k/2 (m=0,1,2, . . .) and even k, but no Nth-order quantum squeezing for other values of N and k; (4) for k\ensuremath{\ge}3, all of them exhibit the lowest- and higher-order quantum antibunching.

Quantum statistical properties of orthonormalized eigenstates of the operator (â f (

\hat n

))k

Eigenstates of the Operator

a_{qs}^k

and Their Antibunching Effect