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A simple, and elegant geometrical representation is developed to describe the concept of coherence and squeezing for angular momentum operators. Angular momentum squeezed states were obtained by applying Bogoliubov transformation on the angular momentum coherent states in Schwinger representation [Phys. Rev. {\bf{A 51}} (1995)]. We present the geometrical phase space description of angular momentum coherent and squeezed states and relate with the harmonic oscillator. The unique feature of our geometric representation is the portraying of the expectation values of the angular momentum components accompanied by their uncertainties. The bosonic representation of the angular momentum coherent and squeezed states is compared with the conventional one mentioning the advantages of this representation of angular momentum in context of coherence and squeezing. Extension of our work on single mode squeezing to double mode squeezing is presented and compared with the single mode one. We also point out the possible applications of the geometrical representation in analyzing the accuracy of interferometers and in studying the behavior, dynamics of an ensemble of quantum-mechanical two-level systems and its interaction with radiation., Comment: RevTeX, tightened preprint, 13 pages. Figs 1(a-d) in separate eps files, figs 2-3 in picture environment within the main LaTeX file

We provide a group-theoretical classification of the entangled states of N identical particles. The connection between quantum entanglement and the exchange symmetry of the states of N identical particles is made explicit using the duality between the permutation group and the simple unitary group. Each particle has n-levels and spans the n-dimensional Hilbert space. We shall call the general state of the particle as a qunit. The direct product of the N qunit space is given a decomposition in terms of states with definite permutation symmetry. The nature of fundamental entanglement of a state can be related to the classes of partitions of the integer N. The maximally entangled states are generated from linear combinations of the less entangled states of the direct product space. We also discuss the nature of maximal entanglement and its measures., Comment: 12 pages, 1 figure

We explore the connection between quantum entanglement and the exchange symmetry of the states of N identical particles. Each particle has n-levels. The N particles span the nN dimensional Hilbert space. We shall call the general state of the particle as a qunit. The direct product of the N qunit space is given a decomposition in terms of states with definite permutation symmetry that are found to have a measure of entanglement which is related to the representation of the permutation group. The maximally entangled states are generated from the linear combinations of fully correlated but unentangled states. The states of lower entanglement are generated from the manifold of partially correlated states. The degree of exchange symmetry is found to be related to a group theoretical measure of entanglement. Email: Jagdish_Rai@hotmail.com, jrai@iitk.ac.in Email: srai56@hotmail.com, Comment: 11 pages, typed in ms-word 2000

We consider the effect of spatial correlations on sources of polarized electromagnetic radiation. The sources, assumed to be monochromatic, are constructed out of dipoles aligned along a line such that their orientation is correlated with their position. In one representative example, the dipole orientations are prescribed by a generalized form of the standard von Mises distribution for angular variables such that the azimuthal angle of dipoles is correlated with their position. In another example the tip of the dipole vector traces a helix around the symmetry axis of the source, thereby modelling the DNA molecule. We study the polarization properties of the radiation emitted from such sources in the radiation zone. For certain ranges of the parameters we find a rather striking angular dependence of polarization. This may find useful applications in certain biological systems as well as in astrophysical sources., Comment: 12 pages, 8 postscript figures

In this paper we analyze the quantum uncertainties and the photon statistics in the interaction between the two modes of radiation by treating them as coupled harmonic oscillator with the motivation of controlling quantum properties of one light beam by another. Under the rotating wave approximation (RWA) we show that if initially one of the modes is coherent and the other one squeezed, then the squeezing and non-Poissonianness of the photon statistics can transfer from one mode to the other. We give a parametric study of these properties depending upon interaction time and the degree of initial squeezing in one of the modes., Comment: RevTex, 7pages preprint, figures available on request to abir@iitk.ernet.in, replaced version is same but without some LaTex corrextions

We propose a simple experimental procedure to produce squeezing and other non-classical properties like photon antibunching of radiation, and amplification without population inversion. The method also decreases the uncertainties of the angular-momentum quadratures representing the two-level atomic system in the interaction of the two-level atoms with quantized radiation., Comment: 9 pages, RevTex,3 LaTex figures, available by sending email to abir@iitk.ernet.in, minor typos changed which is important in physical variables