Hypergeometric States and Their Nonclassical Properties

`Hypergeometric states', which are a one-parameter generalization of binomial states of the single-mode quantized radiation field, are introduced and their nonclassical properties are investigated. Their limits to the binomial states and to the coherent and number states are studied. The ladder operator formulation of the hypergeometric states is found and the algebra involved turns out to be a one-parameter deformation of $su(2)$ algebra. These states exhibit highly nonclassical properties, like sub-Poissonian character, antibunching and squeezing effects. The quasiprobability distributions in phase space, namely the $Q$ and the Wigner functions are studied in detail. These remarkable properties seem to suggest that the hypergeometric states deserve further attention from theoretical and applicational sides of quantum optics.Comment: 17 pages, latex, 7 EPS figure

Negative Binomial and Multinomial States: probability distributions and coherent states

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. Explicit forms of the negative binomial (multinomial) states are given in terms of various boson representations which are naturally related to the probability theory interpretation. Here we show fruitful interplay of probability theory, group theory and quantum theory.Comment: 24 pages, latex, no figure

Pair Superfluid and Supersolid of Correlated Hard-Core Bosons on a Triangular Lattice

We have systematically studied the hard-core Bose-Hubbard model with correlated hopping on a triangular lattice using density-matrix renormalization group method. A rich ground state phase diagram is determined. In this phase diagram there is a supersolid phase and a pair superfluid phase due to the interplay between the ordinary frustrated boson hopping and an unusual correlated hopping. In particular, we find that the quantum phase transition between the supersolid phase and the pair superfluid phase is continuous.Comment: 5.5 pages, 5 figure