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理论物理通讯：英文版

A New Kind of k-Quantum Nonlinear Coherent States： Their Generation and PhysicalMeaning

WANGJi-Suo, LIUTang-Kun, FENGJian, SUNJin-Zuo, ZHANMing-sheng

Published Jan 1, 2004• 0 citations
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Abstract

A new kind of k-quantum nonlinear coherent states, i.e., the κ eigenstates of the κ-th power B^κ (κ>_ 3) of the generalized annihilation operator B=a 1/f(N) of f-oscillators, are obtained and their properties are discussed. The completeness of the κ states is investigated. An alternative method to construct them is proposed. It is shown that these states may form a complete Hilbert space, and all of them can be generated by a linear superposition of κ Roy-type nonlinear coherent states. Physically, they can be generated by a linear superposition of the time-dependent Roy-type nonlinear coherent states at different instants.

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A new kind of k-quantum nonlinear coherent states, i.e., the k eigenstates of the k-th power of the generalized annihilation operator of f-oscillators, are obtained and their properties are discussed. The completeness of the k states is investigated. An alternative method to construct them is proposed. It is shown that these states may form a complete Hilbert space, and all of them can be generated by a linear superposition of k Roy-type nonlinear coherent states. Physically, they can be generated by a linear superposition of the time-dependent Roy-type nonlinear coherent states at different instants.
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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.