Necessary and Sufficient Classicality Conditions on Photon Number Distributions

We exploit results on the classical Stieltjes moment problem to obtain completely explicit necessary and sufficient conditions for the photon number distribution p(n) of a radiation field mode to be classical. These conditions are given in two forms - respectively local and global in the individual photon number probabilities. Central to the first approach is the recognition of the important fact that the quantities n!p(n) are moments of a quasiprobability distribution, notwithstanding the fact that p(n)'s can by themselves be considered as a probability distribution over the nonnegative integers. This leads to local classicality conditions involving p(n)'s for only a small number of values of n. This local approach enables us to present detailed quantitative statements on the connection between nonclassicality and oscillations in the photon number distribution. The second approach is in terms of the traditional factorial moments of p(n). Equivalence of the two approaches is established.Comment: 12-pages in revtex with three ps figure included using eps

The Sampling Theorem and Coherent State Systems in Quantum Mechanics

The well known Poisson Summation Formula is analysed from the perspective of the coherent state systems associated with the Heisenberg--Weyl group. In particular, it is shown that the Poisson summation formula may be viewed abstractly as a relation between two sets of bases (Zak bases) arising as simultaneous eigenvectors of two commuting unitary operators in which geometric phase plays a key role. The Zak bases are shown to be interpretable as generalised coherent state systems of the Heisenberg--Weyl group and this, in turn, prompts analysis of the sampling theorem (an important and useful consequence of the Poisson Summation Formula) and its extension from a coherent state point of view leading to interesting results on properties of von Neumann and finer lattices based on standard and generalised coherent state systems.Comment: 20 pages, Late

Nonclassicality and the concept of local constraints on the photon number distribution

We exploit results from the classical Stieltjes moment problem to bring out the totality of all the information regarding phase insensitive nonclassicality of a state as captured by the photon number distribution p_n. Central to our approach is the realization that n !p_n constitutes the sequence of moments of a (quasi) probability distribution, notwithstanding the fact that p_n can by itself be regarded as a probability distribution. This leads to classicality restrictions on p_n that are local in n involving p_n's for only a small number of consecutive n's, enabling a critical examination of the conjecture that oscillation in p_n is a signature of nonclassicality.Comment: Five pages in revtex with one ps figure included using eps

Facile fabrication of lateral nanowire wrap-gate devices with improved performance

We present a simple fabrication technique for lateral nanowire wrap-gate devices with high capacitive coupling and field-effect mobility. Our process uses e-beam lithography with a single resist-spinning step, and does not require chemical etching. We measure, in the temperature range 1.5-250 K, a subthreshold slope of 5-54 mV/decade and mobility of 2800-2500 $cm^2/Vs$ -- significantly larger than previously reported lateral wrap-gate devices. At depletion, the barrier height due to the gated region is proportional to applied wrap-gate voltage.Comment: 3 pages, 3 figure