Excited Binomial States and Excited Negative Binomial States of the Radiation Field and Some of Their Statistical Properties

We introduce excited binomial states and excited negative binomial states of theradiation field by repeated application of the photon creation operator on binomialstates and negative binomial states. They reduce to Fock states and excitedcoherent states in certain limits and can be viewed as intermediate states betweenFock states and coherent states. We find that both the excited binomial statesand excited negative binomial states can be exactly normalized in terms ofhypergeometric functions. Base on this interesting characteristic, some of thestatistical properties are discussed.     

Dynamical Properties of Some Statistical Quantities for a Quantum System in Generalized Negative Binomial States

We estimate the quantum state of a qubit and a quantized radiation field yielding a generalized negative binomial distribution (GNBD). We give an explicit form for various generalized negative binomial states associated to superposition, even, odd, and q-deformed states. We investigate the dynamical properties of the Mandel parameter as a quantifier of the statistical properties for the radiation field corresponding to its dynamics. We obtain the quantum Fisher information based on the estimation of the atomic state and compare it with the Mandel parameter for different instances of the GNBD. The link between the statistical quantities for different parameters of the GNBD is explored.     

Even and Odd Nonlinear Negative Binomial States

In this paper the even and odd nonlinear negative binomial states of the radiation field are introduced. These states interpolates between even (odd) number states and the even (odd) nonlinear coherent states. The Glauber second-order correlation function is calculated for these states. The squeezing phenomenon (normal and amplitude-squared squeezing), the quasi-probability distribution function Q-function, Wigner-function and the phase properties, are also discussed. Examination of the resonance fluorescence against the present state is given. It has been shown that the atomic inversion is sensitive to any variation in the even and odd nonlinear negative binomial number M and the nonlinearity parameter η.     

位移二项式态与位移负二项式态的性质及其与二能级原子的相互作用

提出并研究两种新的量子光场态：位移二项式态和位移负二项式态．讨论了两种量子态的光子数分布、亚泊松分布特性．结果表明：位移二项式态是介于相干态与位移粒子数态之间的一种量子中间态，在不同参数下可表现亚泊松分布和超泊松分布；位移负二项式态是介于相干态与位移Susking Glogower位相态之间的量子中间态，它只表现超泊松分布．研究了它们与二能级原子在强度耦合情况下相互作用原子反转的动力学演化. 关键词：     

Nonclassical properties and algebraic characteristics of negative binomial states in quantized radiation fields

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 Perelomov'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 geometric states. We also point out that they can be recognized as the nonlinear coherent states. Their nonclassical properties, such as sub-Poissonian distribution and squeezing effect are discussed. The quasiprobability distributions in phase space, namely the Q and Wigner functions, are studied in detail. We also propose two methods of generation of the negative binomial states. d 32.80.Pj Optical cooling of atoms; trapping Received 8 May 1999 and Received in final form 8 November 1999     

Quantum Properties of Odd Excited Negative Binomial States of the Radiation Field

The odd excited negative binomial states are introduced using the photon creation operator by repeated application on negative binomialstates. These states interpolate between the odd displaced Fock states and the odd excited pure thermal states. In this paper both squeezing phenomena (normal squeezing and amplitude squared squeezing) are discussed. Besides discussion of the Glauber second-order correlation function, investigations are carried out for the quasi-probability distribution functions (Wigner function and Q-function). Finally the Pegg-Barnett phase probability distribution is computed for these states.     

Statistical Properties and Algebraic Characteristics of Quantum Superpositions of Negative Binomial States

We introduce new kinds of states of quantized radiation fields,which are the superpositions of megative binomial states.They exhibit remarkable nonclassical properties and reduce to Schrodinger 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 the same eigenvalue equation with the same eigenvalue and they can be viewed as two-photon nonlinear coherent states.Two methods of generating such the states are proposed.     

Wigner Function of Density Operator for Negative Binomial Distribution

By using the technique of integration within an ordered product （IWOP） of operator we derive Wigner function of density operator for negative binomial distribution of radiation field in the mixed state case, then we derive the Wigner function of squeezed number state, which yields negative binomial distribution by virtue of the entangled state representation and the entangled Wigner operator.     

Tomography of Binomial States of the Radiation Field

The symplectic, optical, and photon-number tomographic symbols of binomial states of the radiation field are studied. Explicit relations for all tomograms of the binomial states are obtained. Two measures for nonclassical properties of these states are discussed.     

Correspondence between generalized binomial field states and coherent atomic states

We show that the N-photon generalized binomial states of electromagnetic field may be put in a bijective mapping with the coherent atomic states of N two-level atoms. We exploit this correspondence to simply obtain both known and new properties of the N-photon generalized binomial states. In particular, an over-complete basis of these binomial states and an orthonormal basis are obtained. Finally, the squeezing properties of generalized binomial state are analyzed.     

Influence of the virtual photon field on the squeezing properties of atom laser

This paper investigates the squeezing properties of an atom laser without rotating-wave approximation in the system of a binomial states field interacting with a two-level atomic Bose--Einstein condensate. It discusses the influences of atomic eigenfrequency, the interaction intensity between the optical field and atoms,parameter of the binomial states field and virtual photon field on the squeezing properties. The results show that two quadrature components of an atom laser can be squeezed periodically. The duration and the degree of squeezing an atom laser have something to do with the atomic eigenfrequency and the parameter of the binomial states field, respectively. The collapse and revival frequency of atom laser fluctuation depends on the interaction intensity between the optical field and atoms. The effect of the virtual photon field deepens the depth of squeezing an atom laser.     

Higher order antibunching in intermediate states

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 is predicted in only one type of intermediate state, which is known as shadowed negative binomial state. Recently we have shown that the higher order antibunching is not a rare phenomenon [P. Gupta, P. Pandey, A. Pathak, J. Phys. B 39 (2006) 1137]. To establish our earlier claim further, here we have shown that the higher order antibunching can be seen in different intermediate states, such as binomial state, reciprocal binomial state, hypergeometric state, generalized binomial state, negative binomial state and photon added coherent state. We have studied the possibility of observing the higher order subpoissonian photon statistics in different limits of intermediate states. The effects of different control parameters on the depth of non classicality have also been studied in this connection and it has been shown that the depth of nonclassicality can be tuned by controlling various physical parameters.     

Constructing Even- and Odd-Negative Binomial States

By suitably choosing the normalization factors we introduce the even- and odd-negative binomial states. In some limit cases they approach the even- and odd-coherent states, respectively. We also derive a new eigenvector equation that the negative binomial state satisfies as a nonlinear coherent state.     

Negative binomial multiplicity distribution from binomial cluster production

Two step interpretation of negative binomial multiplicity distribution as a compound of binomial cluster production and negative binomial like cluster decay distribution is proposed. In this model we can expect the average multiplicity for the cluster production increases with increasing energy, different from a compound Poisson-Logarithmic distribution in [4, 5].     

Random cascading models and the link between long-range and short-range interactions in multiparticle production

A general recursive relation for the total multiplicity distribution is derived from a random cascading model with intermittency. The conditions for the existence of a fixed point solution are formulated. An explicit example of such a solution, corresponding to the negative binomial multiplicity distribution is presented. The intimate connection between random cascading models and models of disordered systems is explained and explored. Long-distance properties of the interaction are related to the spectrum of states describing the interaction at short range.     

Statistical properties of the nonlinear negative binomial state

In this context, we introduce and investigate the properties of the nonlinear negative binomial state (the state which interpolates between the nonlinear coherent and the number states). Mainly we concentrate on the statistical properties for such state where we have discussed two different cases of squeezing phenomenon. The first case is the normal squeezing while the second is the amplitude squared squeezing, further the second order correlation function is also considered. Our discussion have been extended to include the quasi-probability distribution functions (W-Wigner and Q-functions). The quadrature distribution and the phase properties in Pegg-Barnett formalism besides the phase variances are considered. Examination of the resonance fluorescence against the present state is given (single atom and thermodynamic limit). It has been shown that the atomic inversion is sensitive to any variation in the nonlinear negative binomial number m.     

Possible evidence for deconfinement in hadron collisions

The collision of hadrons at very high energies produces an entity whose energy density is extremely large resulting in the emission of a large number of hadrons. Though the entity may not have transited into the deconfined parton phase, the very high energy density may cause more than one charged hadron to be emitted at any instant. This yields a new multiplicity distribution, termed the GS distribution which fits the data as well as the popular negative binomial distribution. Neither the GS nor the NB distribution alone agrees with the data beyond 200 GeV, but a weighted sum of GS and NB distributions fits the experimental results exceedingly well. Since the negative binomial distribution arises from the branching of partons, we interpret the increase with energy of the negative binomial component in the weighted sum as the onset of a deconfined phase. The rising cross section for the negative binomial component parallels very closely the inclusive cross section for hadron jets which also is considered a consequence of parton branching.     

内禀退相干下二项式光场与原子互作用的场熵演化

通过求解系统的Milburn 方程,研究了二项式光场与二能级原子相互作用系统中的场熵演化特性,讨论了内禀退相干、二项式光场系数和场的最大光子数对场熵演化的影响.结果表明二项式光场处于中间态时,由于内禀退相干,场熵振荡准周期性减弱,并随着时间的演化,场与原子纠缠逐渐趋近于一个定值,说明存在內禀退相干时,场与原子仍能纠缠;当內禀退相干因子不变时,二项式光场从相干态过渡到中间态,直至数态过程中,场熵值减小,场与原子的纠缠减弱.     

二项式光场和负二项式光场与耦合双原子依赖强度耦合系统原子反转的时间演化

研究了二项式光场和负二项式光场与耦合双原子依赖强度耦合相互作用系统原子布居反转的时间演化规律,讨论了原子间相互作用和光场初态对原子反转的时间演化的影响.     

Comparing energy difference and fidelity of quantum states

We look for upper bounds of the relative energy difference of two pure quantum states with a fixed fidelity between them or upper bounds of the fidelity for a fixed relative energy difference. The results depend on the concrete families of states chosen for the comparison. Exact analytical expressions are found for several popular sets of states: coherent, squeezed vacuum, binomial, negative binomial, and coherent phase states. Their consequence is that to guarantee, for example, a relative energy difference less than 10% for quite arbitrary (unknown) coherent states, the fidelity must exceed the level 0.995. For other kinds of states, the restrictions can be much stronger.