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Physical Review A

Bunching and antibunching properties of various coherent states of the radiation field

M. H. Mahran, M. Venkata Satyanarayana

Published Jul 1, 1986• 29 citations
Publisher

Abstract

In contrast to coherent states \ensuremath{\Vert}\ensuremath{\alpha}〉 which have zero Hanbury Brown and Twiss Effect [i.e., ${g}^{(2)}$(0)=1], it is shown that generalized coherent states \ensuremath{\Vert}n,\ensuremath{\alpha}〉 are antibunched for \ensuremath{\Vert}\ensuremath{\alpha}${\ensuremath{\Vert}}^{2}$(1/2). The range of values for \ensuremath{\alpha} (real) in terms of the squeezing parameter r (real) for the squeezed coherent state \ensuremath{\Vert}\ensuremath{\alpha},r〉 in order to exhibit bunching and antibunching are obtained. The conditions and the exact range of values for r and \ensuremath{\alpha} for a given n for generalized squeezed coherent states \ensuremath{\Vert}n,\ensuremath{\alpha},r〉 to exhibit bunching and antibunching are also obtained.

DOI
10.1103/physreva.34.640

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In contrast to coherent states \ensuremath{\Vert}\ensuremath{\alpha}〉 which have zero Hanbury Brown and Twiss Effect [i.e., g(2){g}^{(2)}g(2)(0)=1], it is shown that generalized coherent states \ensuremath{\Vert}n,\ensuremath{\alpha}〉 are antibunched for \ensuremath{\Vert}\ensuremath{\alpha}\ensuremath∥2{\ensuremath{\Vert}}^{2}\ensuremath∥2(1/2). The range of values for \ensuremath{\alpha} (real) in terms of the squeezing parameter r (real) for the squeezed coherent state \ensuremath{\Vert}\ensuremath{\alpha},r〉 in order to exhibit bunching and antibunching are obtained. The conditions and the exact range of values for r and \ensuremath{\alpha} for a given n for generalized squeezed coherent states \ensuremath{\Vert}n,\ensuremath{\alpha},r〉 to exhibit bunching and antibunching are also obtained.
The generalized even and odd coherent states of a q-Deformation Non-harmonic Oscillator(E-O q-NHCSs) are constructed,their Higher-Order Squeezing and Antibunching Properties are studied in detail.It is increasing the Squeezing effect in different parameter ranges.With q-deformation increasing,the squeezing effect of E q-NHCSs are weakened and those of O q-NHCSs are enhanced.The E q-NHCSs appear high-order(N≥2) antibunching properties while the O q-NHCSs appear high-order bunching properties in some ranges of the parameter q and r 2 with the q-deformation increasing.Both antibunching effects of E q-NHCSs and bunching effects of O q-NHCSs are enhanced.
A new class of non-classical state of the radiation field,called as two-mode squeezed superposed coherent state,is described in this paper.It is defined as ｜φ〉=CS(ξ)(｜α_1,α_2〉+e~(iφ)｜α~*_1,α~*_2〉).Calculating its normalized constant,its non-classical nature is discussed,including squeezed effect,sub-Poissonian distributing,anti-bunching effect,and the second-order cross correlation function between the two-mode.Numerical results demonstrate that the two-mode squeezed superposed coherent state possesses more obvious non-classical properties.Selecting suitable parameters α_1,α_2,φ,θandξ,the two-mode squeezed superposed coherent state can be reduced to the two-mode squeezed superposed vacuum state and the two-mode superposed coherent state.Therefore it is a kind of more generalized non-classical quantum state.
The concept of photon antibunching as a manifestation of nonclassical character in single-mode radiation is extended to two-mode radiation. A simple criterion for the existence of nonclassical effects in two-mode radiation is established. It implies that the intermode photon bunching, rather than antibunching, can play a key role in rendering two-mode radiation nonclassical. The two-mode squeezed vacuum states are used as simple examples to illustrate the essential point of the criterion. The criterion is then used to study the nonclassical properties of two types of two-mode squeezed states. A state generated by applying the squeeze operator to the two-mode vacuum first, followed by the displacement operator, is called a two-mode coherent squeezed state. If the order of the two operators is reversed, a two-mode squeezed coherent state is obtained. It is found that the latter has a much stronger tendency to become a nonclassical state than the former, assuming that the parameters involved are all the same. A measure of nonclassical depth of radiation is adopted. It is found that, according to this measure, the effect of squeezing in making two-mode coherent squeezed states nonclassical is not monotonic. Such phenomena do not occur in squeezed coherent states.
We construct a class of nonlinear coherent states (NLCSs) by introducing a more general nonlinear function and study their nonclassical properties, specifically the second-order correlation function [Formula: see text], Mandel parameter Q, squeezing, amplitude-squared squeezing and Wigner function of the optical field. The results indicate that the nonclassical properties of the new types of even and odd NLCSs crucially depend on the nonlinear functions. More concretely, we find that the new even NLCSs could exhibit the photon-bunching effect, whereas the new odd NLCSs could show the photon-antibunching effect. The degree of squeezing is also significantly affected by the parameter selection of these NLCSs. By employing various forms of nonlinear functions, it becomes possible to construct the NLCSs with diverse properties, thereby providing a theoretical foundation for the corresponding experimental investigations.