Liu Tang-Kun, Wu Pan-Pan, Shan Chuan-Jia, Liu Ji-Bing, Fan Hong-Yi
We find time evolution law of negative binomial optical field in diffusion channel. We reveal that by adjusting the diffusion parameter, photon number can controlled. Therefore, the diffusion process can be considered a quantum controlling scheme through photon addition.
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We introduce excited binomial states and excited negative binomial states of the radiation field by repeated application of the photon creation operator on binomial states and negative binomial states. They reduce to Fock states and excited coherent states in certain limits and can be viewed as intermediate states between Fock states and coherent states. We find that both the excited binomial states and excited negative binomial states can be exactly normalized in terms of hypergeometric functions. Base on this interesting character, some of the statistical properties are discussed.
Following the relationship between probability distribution and coherent states, for example the well known Poisson distribution and the ordinary coherent states and relatively less known one of the binomial distribution and the $su(2)$ coherent states, we propose ``interpretation'' of $su(1,1)$ and $su(r,1)$ coherent states ``in terms of probability theory''. They will be called the ``negative binomial'' (``multinomial'') ``states'' which correspond to the ``negative'' binomial (multinomial) distribution, the non-compact counterpart of the well known binomial (multinomial) distribution. Expli…
We introduce new kinds of states of quantized radiation fields, which are the superpositions of negative binomial states. They exhibit remarkable non-classical properties and reduce to Schrödinger cat states in a certain limit. The algebras involved in the even and odd negative binomial states turn out to be generally deformed oscillator algebras. It is found that the even and odd negative binomial states satisfy a same eigenvalue equation with a same eigenvalue and they can be viewed as two-photon nonlinear coherent states. Two methods of generating such states are proposed.
We show that the well-known negative binomial states of the radiation field and their excitations are nonlinear coherent states. Excited nonlinear coherent state are still nonlinear coherent states with different nonlinear functions. We finally give exponential form of the nonlinear coherent states and remark that the binomial states are not nonlinear coherent states.
We introduce the negative binomial states with negative binomial distribution as their photon number distribution. They reduce to the ordinary coherent states and Susskind-Glogower phase states in different limits. The ladder and displacement operator formalisms are found and they are essentially the Perelomov's su(1,1) coherent states via its Holstein-Primakoff realisation. These states exhibit strong squeezing effect and they obey the super-Poissonian statistics. A method to generate these states is proposed.
We study the nonclassical properties and algebraic characteristics of the negative binomial states introduced by Barnett recently. The ladder operator formalism and displacement operator formalism of the negative binomial states are found and the algebra involved turns out to be the SU(1,1) Lie algebra via the generalized Holstein-Primarkoff realization. These states are essentially Peremolov's SU(1,1) coherent states. We reveal their connection with the geometric states and find that they are excited geometric states. As intermediate states, they interpolate between the number states and geom…
We show that the three quantum states (P$\acute{o}$lya states, the generalized non-classical states related to Hahn polynomials and negative hypergeometric states) introduced recently as intermediates states which interpolate between the binomial states and negative binomial states are essentially identical. By using the Hermitial-phase-operator formalism, the phase properties of the hypergeometric states and negative hypergeometric states are studied in detail. We find that the number of peaks of phase probability distribution is one for the hypergeometric states and $M$ for the negative hype…
The completeness of quantum state space, is usually expressed as \sum_{m=0}^{\infty}|m><m|=1, where {|m>} is selected set of quantum states (basis). Density matrix |m><m| describes a pure quantum state. In this paper, by virtue of the summation method within the normally ordered product of operators we propose and show that the completeness relation can also be represented or partitioned in terms of some mixed states, such as binomial states and negative binomial states. Thus the view on the structure of Fock space is widen and the connotation of Fock space is enriched. See the matter in this …
Since the introduction of binomial state as an intermediate state, different intermediate states have been proposed. Different nonclassical effects have also been reported in these intermediate states. But till now higher order antibunching or higher order subpoissonian photon statistics is predicted only in one type of intermediate state, namely shadowed negative binomial state. Recently we have shown the existence of higher order antibunching in some simple nonlinear optical processes to establish that higher order antibunching is not a rare phenomenon (J. Phys. B 39 (2006) 1137). To establi…
The click statistics from on-off detector systems is quite different from the counting statistics of the more traditional detectors. This necessitates introduction of new parameters to characterize the nonclassicality of fields from measurements using on-off detectors. To properly replace the Mandel Q_M parameter, we introduce a parameter Q_B. A negative value represents a sub-binomial statistics. This is possible only for quantum fields, even for super-Poisson light. It eliminates the problems encountered in discerning nonclassicality using Mandel's Q_M for on-off data.
A phase space localization operator in negative binomial states
本文研究负二项式态下半径 R<1 圆盘相空间局域化算子 P_R，借助伪谐振子、光子计数分布与相干态变换给出其 Bergman 空间积分核，并实现 Hilbert 空间随 R 的自然推广。
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