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Nonclassical properties of the orthonormalized eigenstates of the operator ((a)over-cap-f((n)over-cap))(k)

Jian‐Sheng Wang, Jie Feng, TK Liu, Zhan Zhan

Published Sep 1, 2002• 0 citations
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Abstract

The completeness of the k orthonormalized eigenstates of the operator ((a) over capf((n) over cap))(k)(k greater than or equal to 3) is investigated. We introduce an antibunching and a new kind of higher-order squeezing. The properties of the antibunching effect and M-th-order squeezing of the k states are studied. The result shows that these states may form a complete Hilbert space. There is antibunching effect in all of the states, and the M-th [M = ( n + 1/2) k; n = 0, 1 2, ...] squeezing effects exist in all of the k states when k is even.

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The completeness of the k orthonormalized eigenstates of the operator ((a) over capf((n) over cap))(k)(k greater than or equal to 3) is investigated. We introduce an antibunching and a new kind of higher-order squeezing. The properties of the antibunching effect and M-th-order squeezing of the k states are studied. The result shows that these states may form a complete Hilbert space. There is antibunching effect in all of the states, and the M-th [M = ( n + 1/2) k; n = 0, 1 2, ...] squeezing effects exist in all of the k states when k is even.
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A new kind of nonlinear coherent states, i.e. the k eigenstates of the powers B^k (k ≥ 3) of the generalized annihilation operator B^=a^†-1f(N^) of f-oscillators, are constructed using the inverse operators of the boson annihilation and creation operators. The set of these states may form a complete quantum mechanics representation. Using newly defined higher order squeezing and an antibunching, the properties of the Mth-order squeezing and the antibunching effect of the k states are investigated. The results show that the Mth-order [M = (n + 1/2)k; n = 0, 1, 2, …] squeezing effects exist in all of the k states when k is even and the antibunching effect exists in all of the k states.