Entanglement criteria via the uncertainty relations in su(2) and su(1,1) algebra: detection of non-Gaussian entangled states

We derive a class of inequalities, from the uncertainty relations of the SU(1,1) and the SU(2) algebra in conjunction with partial transposition, that must be satisfied by any separable two-mode states. These inequalities are presented in terms of the su(2) operators J_x, J_y, and the total photon number N_a+N_b. They include as special cases the inequality derived by Hillery and Zubairy [Phys. Rev. Lett. 96, 050503 (2006)], and the one by Agarwal and Biswas [New J. Phys. 7, 211 (2005)]. In particular, optimization over the whole inequalities leads to the criterion obtained by Agarwal and Biswas. We show that this optimal criterion can detect entanglement for a broad class of non-Gaussian entangled states, i.e., the su(2) minimum-uncertainty states. Experimental schemes to test the optimal criterion are also discussed, especially the one using linear optical devices and photodetectors.Comment: published version, presentation polished with references added, 7 pages, 4 figure

Single-shot measurement of quantum optical phase

Although the canonical phase of light, which is defined as the complement of photon number, has been described theoretically by a variety of distinct approaches, there have been no methods proposed for its measurement. Indeed doubts have been expressed about whether or not it is measurable. Here we show how it is possible, at least in principle, to perform a single-shot measurement of canonical phase using beam splitters, mirrors, phase shifters and photodetectors.Comment: This paper was published in PRL in 2002 but, at the time, was not placed on the archive. It is included now to make accessing this paper easie

Cosmological Perturbations of Quantum-Mechanical Origin and Anisotropy of the Microwave Background

Cosmological perturbations generated quantum-mechanically (as a particular case, during inflation) possess statistical properties of squeezed quantum states. The power spectra of the perturbations are modulated and the angular distribution of the produced temperature fluctuations of the CMBR is quite specific. An exact formula is derived for the angular correlation function of the temperature fluctuations caused by squeezed gravitational waves. The predicted angular pattern can, in principle, be revealed by the COBE-type observations.Comment: 9 pages, WUGRAV-92-17 Accepted for Publication in Phys. Rev. Letters (1993

Phase properties of hypergeometric states and negative hypergeometric states

We show that the three quantum states (P$\acute{o}$lya states, the generalized non-classical states related to Hahn polynomials and negative hypergeometric states) introduced recently as intermediates states which interpolate between the binomial states and negative binomial states are essentially identical. By using the Hermitial-phase-operator formalism, the phase properties of the hypergeometric states and negative hypergeometric states are studied in detail. We find that the number of peaks of phase probability distribution is one for the hypergeometric states and $M$ for the negative hypergeometric states.Comment: 7 pages, 4 figure

Linear amplification and quantum cloning for non-Gaussian continuous variables

We investigate phase-insensitive linear amplification at the quantum limit for single- and two-mode states and show that there exists a broad class of non-Gaussian states whose nonclassicality survives even at an arbitrarily large gain. We identify the corresponding observable nonclassical effects and find that they include, remarkably, two-mode entanglement. The implications of our results for quantum cloning outside the Gaussian regime are also addressed.Comment: published version with reference updat

Statistics of Raman-Active Excitations via Masurement of Stokes-Anti-Stokes Correlations

A general fundamental relation connecting the correlation of Stokes and anti-Stokes modes to the quantum statistical behavior of vibration and pump modes in Raman-active materials is derived. We show that under certain conditions this relation can be used to determine the equilibrium number variance of phonons.Time and temperature ranges for which such conditions can be satisfied are studied and found to be available in todays' experimental standards. Furthermore, we examine the results in the presence of multi-mode pump as well as for the coupling of pump to the many vibration modes and discuss their validity in these cases.Comment: 12 pages, 1 figure, accepted for publication in Phys.Rev.

Novel approach to the study of quantum effects in the early universe

We develop a theoretical frame for the study of classical and quantum gravitational waves based on the properties of a nonlinear ordinary differential equation for a function $\sigma(\eta)$ of the conformal time $\eta$, called the auxiliary field equation. At the classical level, $\sigma(\eta)$ can be expressed by means of two independent solutions of the ''master equation'' to which the perturbed Einstein equations for the gravitational waves can be reduced. At the quantum level, all the significant physical quantities can be formulated using Bogolubov transformations and the operator quadratic Hamiltonian corresponding to the classical version of a damped parametrically excited oscillator where the varying mass is replaced by the square cosmological scale factor $a^{2}(\eta)$. A quantum approach to the generation of gravitational waves is proposed on the grounds of the previous $\eta-$dependent Hamiltonian. An estimate in terms of $\sigma(\eta)$ and $a(\eta)$ of the destruction of quantum coherence due to the gravitational evolution and an exact expression for the phase of a gravitational wave corresponding to any value of $\eta$ are also obtained. We conclude by discussing a few applications to quasi-de Sitter and standard de Sitter scenarios.Comment: 20 pages, to appear on PRD. Already published background material has been either settled up in a more compact form or eliminate

Roper excitation in p⃗+α→p⃗+α+X\vec{p}+\alpha \to \vec{p}+\alpha+X reactions

We calculate differential cross sections and the spin transfer coefficient $D_{nn}$ in the $\vec{p}+\alpha \to \vec{p}+\alpha+\pi^0$ reaction for proton bombarding energies from 1 to 10 GeV and $\pi^0 - p$ invariant masses spanning the region of the N$^*$(1440) Roper resonance. Two processes -- $\Delta$ excitation in the $\alpha$-particle and Roper excitation in the proton -- are included in an effective reaction model which was shown previously to reproduce existing inclusive spectra. The present calculations demonstrate that these two contributions can be clearly distinguished via $D_{nn}$, even under kinematic conditions where cross sections alone exhibit no clear peak structure due to the excitation of the Roper.Comment: 12 pages, 11 ps figures, Late

Position-momentum local realism violation of the Hardy type

We show that it is, in principle, possible to perform local realism violating experiments of the Hardy type in which only position and momentum measurements are made on two particles emanating from a common source. In the optical domain, homodyne detection of the in-phase and out-of-phase amplitude components of an electromagnetic field is analogous to position and momentum measurement. Hence, local realism violations of the Hardy type are possible in optical systems employing only homodyne detection.Comment: 10 pages, no figures, to be published in Physical Review

States interpolating between number and coherent states and their interaction with atomic systems

Using the eigenvalue definition of binomial states we construct new intermediate number-coherent states which reduce to number and coherent states in two different limits. We reveal the connection of these intermediate states with photon-added coherent states and investigate their non-classical properties and quasi-probability distributions in detail. It is of interest to note that these new states, which interpolate between coherent states and number states, neither of which exhibit squeezing, are nevertheless squeezed states. A scheme to produce these states is proposed. We also study the interaction of these states with atomic systems in the framework of the two-photon Jaynes-Cummings model, and describe the response of the atomic system as it varies between the pure Rabi oscillation and the collapse-revival mode and investigate field observables such as photon number distribution, entropy and the Q-function.Comment: 26 pages, 29 EPS figures, Latex, Accepted for publication in J.Phys.