Properties of Squeezed-State Excitations

The photon distribution function of a discrete series of excitations of squeezed coherent states is given explicitly in terms of Hermite polynomials of two variables. The Wigner and the coherent-state quasiprobabilities are also presented in closed form through the Hermite polynomials and their limiting cases. Expectation values of photon numbers and their dispersion are calculated. Some three-dimensional plots of photon distributions for different squeezing parameters demonstrating oscillatory behaviour are given.Comment: Latex,35 pages,submitted to Quant.Semiclassical Op

Radon transform and pattern functions in quantum tomography

The two-dimensional Radon transform of the Wigner quasiprobability is introduced in canonical form and the functions playing a role in its inversion are discussed. The transformation properties of this Radon transform with respect to displacement and squeezing of states are studied and it is shown that the last is equivalent to a symplectic transformation of the variables of the Radon transform with the contragredient matrix to the transformation of the variables in the Wigner quasiprobability. The reconstruction of the density operator from the Radon transform and the direct reconstruction of its Fock-state matrix elements and of its normally ordered moments are discussed. It is found that for finite-order moments the integration over the angle can be reduced to a finite sum over a discrete set of angles. The reconstruction of the Fock-state matrix elements from the normally ordered moments leads to a new representation of the pattern functions by convergent series over even or odd Hermite polynomials which is appropriate for practical calculations. The structure of the pattern functions as first derivatives of the products of normalizable and nonnormalizable eigenfunctions to the number operator is considered from the point of view of this new representation.Comment: To appear on Journal of Modern Optics.Submitted t

Water in the desert? The influence of Wilhelm Röpke on Ludwig Erhard and the social market economy

It is commonly believed that Wilhelm Röpke heavily influenced Ludwig Erhard and, through him, West Germany’s social market economy. This article demonstrates that Röpke’s influence on Erhard was limited. Although the two men shared many common ideals, they also differed on many fundamental issues. Moreover, Erhard developed his ideas before he read Röpke’s wartime trilogy. Copyright Springer Science + Business Media, LLC 2006Social market economy, Ludwig Erhard, Wilhelm Röpke, West Germany,