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Chinese journal of atomic and molecular physics

The internal structure of the eigenstates of the higher order of the annihilation operators for any optical field

Liang Mai

Published Jan 1, 2003• 0 citations
OpenAlex

Abstract

The eigenstates of the higher order of the annihilation operator for any optical field all have even and odd structure just like the even and odd coherent states. According to this result, it is pointed out how to use the eigenstates of a M to generate the eigenstates a 2M for the monomode optical fields.

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A method for construction of the k orthonormalized quantum eigenstates of the higher powers ak{\mathit{a}}^{\mathit{k}}ak 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.