相关论文: Characterization of SU(1,1) coherent states in ter…

A sufficient condition for a state |\psi> to minimize the Robertson-Schr\"{o}dinger uncertainty relation for two observables A and B is obtained which for A with no discrete spectrum is also a necessary one. Such states, called generalized…

We propose a practical recipe to compute the ${s}$-parametrized maps for systems with $SU(1,1)$ symmetry using a connection between the ${Q}$ and ${P} $ symbols through the action of an operator invariant under the group. The particular…

We provide a formula for computing the overlap between two Generalized Coherent States of any rank one simple Lie algebra. Then, we apply our formula to spin coherent states (i.e. $\mathfrak{su}(2)$ algebra), pseudo-spin coherent states…

We construct a new class of coherent states indexed by points z of the complex plane and depending on two positive parameters m and epsilon by replacing the coefficients of the canonical coherent states by polyanalytic functions. These…

Congruences, or $2$-parameter families of lines in $3$-space are of interest in many situations, in particular in geometric optics. In this paper we consider elements of their geometry which are invariant under affine changes of…

We derive the coherent state representation of the integrable spin chain Hamiltonian with supersymmetry group $SU(1,1|2)$. By the use of a projected Hamiltonian onto bosonic states, we give explicitly the action of the Hamiltonian on…

In this paper, we construct the coherent states for a system of an electron moving on plane in uniform external magnetic and electric fields. These coherent states are built in the context of both discrete and continuous spectra and satisfy…

A new kind of q-deformed charged coherent states is constructed in Fock space of two-mode q-boson system with su_{q}(2) covariance and a resolution of unity for these states is derived. We also present a simple way to obtain these coherent…

The method of vector coherent states is generalized to study representations of the affine Lie algebra $\hat{sl}(2)$. A large class of highest weight irreps is explicitly constructed, which contains the integrable highest weight irreps as…

In this paper we discuss a proposal of coherent states for Loop Quantum Gravity. These states are labeled by a point in the phase space of General Relativity as captured by a spin-network graph. They are defined as the gauge invariant…

We study the radial part of the MICZ-Kepler problem in an algebraic way by using the $su(1,1)$ Lie algebra. We obtain the energy spectrum and the eigenfunctions of this problem from the $su(1,1)$ theory of unitary representations and the…

We introduce a generalization structure of the su(1,1) algebra which depends on a function of one generator of the algebra, f(H). Following the same ideas developed to the generalized Heisenberg algebra (GHA) and to the generalized su(2),…

This is a continuation of the preceding paper (hep-ph/0108219). First of all we make a brief review of generalized coherent states based on Lie algebra su(1,1) and prove that the resolution of unity can be obtained by the curvature form of…

An SU(1,1) interferometer replaces the beamsplitters in a Mach-Zehnder interferometer with nonlinear interactions and offers the potential of achieving high phase sensitivity in applications with low optical powers. We present a novel…

We construct a class of generalized phase coherent states indexed by points of the unit circle and depending on three positive parameters "gamma","alpha" and "epsilon" by replacing the labelling coefficients of the canonical coherent states…

We introduce new families of pure quantum states that are constructed on top of the well-known Gilmore-Perelomov group-theoretic coherent states. We do this by constructing unitaries as the exponential of operators quadratic in Cartan…

The quantum correlation of light and atomic collective excitation can be used to compose an SU(1,1)-type hybrid light-atom interferometer, where one arm in optical SU(1,1) interferometer is replaced by the atomic collective excitation. The…

We propose quantum Painlev\'e systems of type $A_l^{(1)}$. These systems, for $l=1$ and $l\ge 2$, should be regarded as quantizations of the second Painlev\'e equation and the differential systems with the affine Weyl group symmetries of…

We introduce and obtain multimode paraboson coherent states. In appropriate subspaces these coherent states provide a decomposition of unity where the measure, when expressed using the cat-type states, is positive definite. Bicoherent…

We theoretically study the phase sensitivity of the SU(1,1) interferometer with a coherent light together with a squeezed vacuum input case using the method of homodyne. We find that the homodyne detection has better sensitivity than the…