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理论物理通讯：英文版

Quantum Statistical Properties of k-Quantum Nonlinear Coherent States

WANGJi-Suo, Ji-Suo, Liu ., Tang-Kun, Feng, Jian JIAN, Sun, Jin-Zuo

Published Jan 1, 2004• 0 citations
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Abstract

In our preceding work, a class of k-quantum nonlinear coherent states, i.e., the k eigenstates of the powersBk (k ≥ 3) of the annihilation operator B=-a1/f(N) of f-oscillators, are introduced. In this paper, we introduce a newkind of higher-order squeezing and an antibunching effect. The quantum statistical properties of the k states are studied.The result shows that the M-th order [M = (n + 1/2)k; n = 0, 1,...] squeezing effects exist in all of the k states when kis even. There is the antibunching effect in all of the k states.

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In our preceding work, a class of k-quantum nonlinear coherent states, i.e., the k eigenstates of the powersBk (k ≥ 3) of the annihilation operator B=-a1/f(N) of f-oscillators, are introduced. In this paper, we introduce a newkind of higher-order squeezing and an antibunching effect. The quantum statistical properties of the k states are studied.The result shows that the M-th order [M = (n + 1/2)k; n = 0, 1,...] squeezing effects exist in all of the k states when kis even. There is the antibunching effect in all of the k states.
In our preceding work, a class of k-quantum nonlinear coherent states, i.e., the k eigenstates of the powers (B) over cap (k) (k greater than or equal to 3) of the annihilation operator (B) over cap = (a) over cap1/f((N) over cap) of f-oscillators, are introduced. In this paper, we introduce a new kind of higher-order squeezing and an antibunching effect. The quantum statistical properties of the k states are studied. The result shows that 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 the antibunching effect in all of the k states.
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.
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.
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 a new kind of higher-order squeezing and an antibunching. The properties of the Mth-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 Mth-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.
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.
A new kind of even and odd nonlinear coherent states are defined. Using the numerical method, we have studied quantum statistical properties of the new even and odd nonlinear coherent states. It is shown that quantum statistical properties of the new even and odd nonlinear coherent states are very different from those of the usual even and odd coherent states. It is found that, in some ranges of 1beta1, the squeezing only exists in the new even nonlinear coherent state, and the amplitude-squared squeezing and antibunching effect appear for both new even and odd nonlinear coherent states.