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Journal of Liuzhou Teachers College

Non-classical Properties for K-th Power Eigen-states of Q-boson Annihilation Operators

Lan Hai-jiang

Published Jan 1, 2012• 0 citations
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Abstract

Non-classical properties for the eigen-states of k-th power of q-boson annihilation operators were calculated by their representations in Fock spaces.The non-classical properties of these eigen-states were further discussed by numerically discussing their quasiprobability distributions in phase spaces.It is shown that the certain non-classical quantum states could be generated from quasiclassical coherent states by q-deformations;these eigen-states are typically non-classical quantum states,as their relevant Wigner functions reveal negatives for certain parameters.

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Non-classical properties for the eigen-states of k-th power of q-boson annihilation operators were calculated by their representations in Fock spaces.The non-classical properties of these eigen-states were further discussed by numerically discussing their quasiprobability distributions in phase spaces.It is shown that the certain non-classical quantum states could be generated from quasiclassical coherent states by q-deformations;these eigen-states are typically non-classical quantum states,as their relevant Wigner functions reveal negatives for certain parameters.
Wigner functions for the eigenstates of arbitrary power of annihilation operators were reconstructed using their expressions in Fock presentations.The distribution of the reconstructed Wigner functions in phase spaces was analyzed,based on which the nonclassical properties of these eigenstates were discussed.The results show that,the distribution of the Wigner functions for these eigenstates depend on the eigenvalues of the annihilation operators;the eignestates of the annihilation operators of the first power(i.e.,coherent states) are quasiclassical(their Wigner functions are always non-negative),and those of higher powers obviously exhibit nonclassical properties(their Wigner functions may become negative).
By using the expression of second-order coherence degree and Wigner function in Fock presentation,the second-order coherence degrees and the Wigner functions of the eigenstates of annihilation operator a3 were calculated.Based on the anti-bunching effect and the distributions of Wigner functions,the nonclassical properties of these eigenstates were analyzed.The numerical results show that these eigenstates produce anti-bunching effect,and their relevant Wigner functions can be negative in phase spaces,which indicates that the eigenstates of annihilation operator a3 are non-classical states.
Wigner functions in phase space are reconstructed for the excited coherent states，which are generated by applying the inverse of k-Boson operators repeatedly to the coherent states. The non-classicality of these states is discussed by calculating their Wigner functions in Fock-state space. Numerical results show that these excited coherent states always reveal non-classical characteristics，no matter whether the excited number k is even or odd，and also the corresponding non-classicality is more obvious with the number k increasing.
We present a detailed discussion of even and odd coherent states defined as eigenstates of the single mode two-photon annihilation operator a 2. We study the non-classical properties such as squeezing, higher-order squeezing, and photon antibunching. Also discussed are the various quantum quasiprobability distributions, namely the P function, which is shown to be highly singular, the Q function, and the Wigner, which can take on negative values for these states. Finally, we present a discussion of a possible mechanism for the generation of such states based on the competition between parametric amplification and the incoherent losses from two-photon resonant absorption.
The k orthonormalized eigenstates of the k th power {( a q f ( N q ))} k ( k ⩾1) of the generalized q -boson annihilation operator a q f ( N q ) are obtained, and their properties are discussed. An alternative method to construct them is proposed, and it is shown that all of them can be expressed as a linear superposition of k q - f -coherent states that have the same amplitude but different phases. Physically, they can be generated by a linear superposition of the time-dependent q - f -coherent states at different instants.