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Coherent states in mathematical physics
About: Coherent states in mathematical physics is a research topic. Over the lifetime, 732 publications have been published within this topic receiving 32024 citations.
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TL;DR: In this paper, the authors briefly review some applications of dynamical Lie algebras and groups and their associated coherent states in quantum optics and molecular spectroscopy, and present a survey of these applications.
Abstract: We briefly review some applications of dynamical Lie algebras and groups and their associated coherent states in quantum optics and molecular spectroscopy.
12 citations
TL;DR: In this article, a method of constructing discrete coherent states for n qubits is proposed, where the coherent states appear as displaced versions of a fiducial vector that is fixed by imposing a number of natural symmetry requirements on its Q-function.
Abstract: We put forward a method of constructing discrete coherent states for n qubits. After establishing appropriate displacement operators, the coherent states appear as displaced versions of a fiducial vector that is fixed by imposing a number of natural symmetry requirements on its Q-function. Using these coherent states, we establish a partial order in the discrete phase space, which allows us to picture some n-qubit states as apparent distributions. We also analyze correlations in terms of sums of squared Q-functions.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’.
12 citations
TL;DR: In this paper, a straightening-free algorithm for computing the canonical bases of any higher-level q-deformed Fock space is presented, where the bases can be computed in any higher level.
12 citations
TL;DR: In this paper, a class of higher-order, three-mode states called K-dimensional trio coherent states were introduced and proved to be complete sets in a truncated Fock space.
Abstract: We introduce a novel class of higher-order, three-mode states called K-dimensional trio coherent states. We study their mathematical properties and prove that they form a complete set in a truncated Fock space. We also study their physical content by explicitly showing that they exhibit nonclassical features such as oscillatory number distribution, sub-Poissonian statistics, Cauchy–Schwarz inequality violation and phase-space quantum interferences. Finally, we propose an experimental scheme to realize the state with K = 2 in the quantized vibronic motion of a trapped ion.
12 citations
TL;DR: In this article, the authors investigated completeness properties of discrete coherent states associated with higher order Euclidean and hyperbolic Landau levels, partially extending classic results of Perelomov and of Bargmann, Butera, Girardello and Klauder.
Abstract: We consider the quantum dynamics of a charged particle evolving under the action of a constant homogeneous magnetic field, with emphasis on the discrete subgroups of the Heisenberg group (in the Euclidean case) and of the SL(2, R) group (in the Hyperbolic case). We investigate completeness properties of discrete coherent states associated with higher order Euclidean and hyperbolic Landau levels, partially extending classic results of Perelomov and of Bargmann, Butera, Girardello and Klauder. In the Euclidean case, our results follow from identifying the completeness problem with known results from the theory of Gabor frames. The results for the hyperbolic setting follow by using a combination of methods from coherent states, time-scale analysis and the theory of Fuchsian groups and their associated automorphic forms.
12 citations