[en] The operator annihilating a single quantum of excitation in a bosonic field is one of the cornerstones for the interpretation and prediction of the behavior of the microscopic quantum world. Here we present a systematic experimental study of the effects of single-photon annihilation on some paradigmatic light states. In particular, by demonstrating the invariance of coherent states by this operation, we provide the first direct verification of their definition as eigenstates of the photon annihilation operator.

[en] We have recently realized experimental schemes to implement the action of single-photon creation and annihilation operators onto completely classical and fully incoherent thermal light states (Parigi et al 2007 Science 317 1890). By applying alternated sequences of the creation and annihilation operators we observed that the resulting states depend on the order in which the two quantum operators are applied, thus obtaining the most direct experimental test of non-commutativity. Here we provide an extensive and detailed discussion of the main experimental issues related to the realization of these schemes.

[en] We consider properties of the operators D(r,M)=a^r(a^†a)^M (which we call generalized Laguerre-type derivatives), with r=1,2,..., M=0,1,..., where a and a^† are boson annihilation and creation operators, respectively, satisfying [a,a^†]=1. We obtain explicit formulas for the normally ordered form of arbitrary Taylor-expandable functions of D(r,M) with the help of an operator relation that generalizes the Dobinski formula. Coherent state expectation values of certain operator functions of D(r,M) turn out to be generating functions of combinatorial numbers. In many cases the corresponding combinatorial structures can be explicitly identified.

[en] The large time dynamics of a two-species coagulation-annihilation system with constant coagulation and annihilation rates is studied analytically when annihilation is complete. A scaling behaviour is observed which varies with the parameter coupling, the annihilation of the two species and which is nonuniversal in the sense that it varies, in some cases, with the initial conditions as well. The latter actually occurs when either the coupling parameter is equal to one, or the initial number of particles is the same for the two species.

[en] We present a scheme to prepare generalized coherent states in a system with two species of Bose-Einstein condensates. First, within the two-mode approximation, we demonstrate that a Schroedinger cat-like state can be dynamically generated and, by controlling the Josephson-like coupling strength, the number of coherent states in the superposition can be varied. Later, we analyze numerically the dynamics of the whole system when interspecies collisions are inhibited. Variables such as fractional population, Mandel parameter and variances of annihilation and number operators are used to show that the evolved state is entangled and exhibits sub-Poisson statistics

[en] In this paper, we give a general discussion on the calculation of the statistical distribution from a given operator relation of creation, annihilation, and number operators. Our result shows that as long as the relation between the number operator and the creation and annihilation operators can be expressed as a^†b=Λ(N) or N=Λ⁻¹(a^†b), where N, a^†, and b denote the number, creation, and annihilation operators, i.e., N is a function of quadratic product of the creation and annihilation operators, the corresponding statistical distribution is the Gentile distribution, a statistical distribution in which the maximum occupation number is an arbitrary integer. As examples, we discuss the statistical distributions corresponding to various operator relations. In particular, besides the Bose–Einstein and Fermi–Dirac cases, we discuss the statistical distributions for various schemes of intermediate statistics, especially various q-deformation schemes. Our result shows that the statistical distributions corresponding to various q-deformation schemes are various Gentile distributions with different maximum occupation numbers which are determined by the deformation parameter q. This result shows that the results given in much literature on the q-deformation distribution are inaccurate or incomplete. -- Highlights: ► A general discussion on calculating statistical distribution from relations of creation, annihilation, and number operators. ► A systemic study on the statistical distributions corresponding to various q-deformation schemes. ► Arguing that many results of q-deformation distributions in literature are inaccurate or incomplete

[en] We introduce the inverse annihilations and creation operators a^-1 and a^†-1 by their actions on the number states. We show that the squeezed vacuum exp[(1/2)ξa^†2] vertical bar 0> and squeezed first number state exp[(1/2)ξa^†2] vertical bar n=1> are respectively the eigenstates of the operators (a^†-1 a) and (aa^†-1) with eigenvalue ξ. (author). 8 refs

[en] We consider an experimentally realizable scheme for manipulating quantum states using a general superposition of products of field annihilation ( a-hat ) and creation (a-hat+) operators. Such an operation, when applied on states with classical features, is shown to introduce strong nonclassicality. We quantify the generated degree of nonclassicality by the negative volume of Wigner distribution in the phase space and investigate two other observable nonclassical features, sub-Poissonian statistics and squeezing. We find that the operation introduces negativity in the Wigner distribution of an input coherent state and changes the Gaussianity of an input thermal state. This provides the possibility of engineering quantum states with specific nonclassical features.

[en] We solve the boson normal ordering problem for (q(a^-bar )a+v(a^-bar ))ⁿ with arbitrary functions q and v and integer n, where a and a^-bar are boson annihilation and creation operators, satisfying [a,a^-bar ]=1. This leads to exponential operators generalizing the shift operator and we show that their action can be expressed in terms of substitutions. Our solution is naturally related through the coherent state representation to the exponential generating functions of Sheffer-type polynomials. This in turn opens a vast arena of combinatorial methodology which is applied to boson normal ordering and illustrated by a few examples

[en] We find and analyze the (nonlinear) supercoherent states associated with the generalized nonlinear supersymmetric annihilation operator (SAO) of the supersymmetric harmonic oscillator. We discuss as well the uncertainty relation for a special case in order to compare our results with those obtained for the linear supercoherent states. (paper)