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Acta Physica Sinica

Wigner functions of multiple-photon excited coherent states

Lan Hai-jiang, Pang Hua-Feng, Lian-Fu Wei, (1)柳州师范高等专科学校物理与信息科学系，柳州 545003；西南交通大学量子光电信息实验室，成都 610031; (2)西南交通大学量子光电信息实验室，成都 610031

Published Jan 1, 2009• 3 citations
Publisher

Abstract

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.

DOI
10.7498/aps.58.8281

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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.
Using the coherent state representation of the Wigner operator, the Wigner function for the photon-added even and odd coherent state (PAEOCS) is obtained. In terms of the variations of the Wigner function with the complex parameter α in the phase space, the non-classical properties of the PAEOCS are discussed. It is found that the PAEOCS always exhibits the non-classical properties, and the photon-added even (or odd) coherent state exhibits the non-classical properties more easily when m is odd (or even). By virtue of the marginal distributions of the Wigner function for the PAEOCS, we illuminate the physical meaning of the Wigner function. Finally, based on the intermidate coordinate-momentum presentation the quantum tomogram function for the PAEOCS is obtained.
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).
The superposition of excited coherent states was constructed by superpositioning two excited coherent states of the same intensity and mutual phase conjugation,and their Wigner functions,second-order coherence degree and Mandel Q factors were calculated,upon which their non-classical properties were analyzed.The numerical results show that,the Wigner functions of the superposition of excited coherent states may become negative,and their second-order coherence degree and Mandel Q factors are both less than 1.Hence,the research shows that the quasi-probability distribution of the superposition of excited coherent states may become negative,and their light field has anti-bunching effects,with the distribution of photon number being of sub-Poisson distribution.Therefore,these superposition states are quantum states with non-classical properties.
Based on the expressions of Wigner functions in Fock-spaces,we reconstruct the Wigner functions of photon-added and-subtracted states of squeezed vacuum states.Negativities of these Wigner functions numerically indicate that these states are really non-classical quantum states.We also discuss how these negativities depend on the photon number k added to and subtraced from the squeezed vacuum states.The negativities are greater when k is odd numbers than those when k is even numbers.The result provides a theoretical foundation for measuring these states.