Topic
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.
Papers published on a yearly basis
Papers
More filters
CERN1
TL;DR: In this article, the authors introduced the concept of coherent states and their properties for simple quantum compact groups, such as Al, Bl, Cl and Dl, and showed that the coherent state can be interpreted as a holomorphic function on this orbit with values in the carrier Hilbert space of an irreducible representation of the corresponding quantized enveloping algebra.
Abstract: Coherent states are introduced and their properties are discussed for simple quantum compact groupsAl, Bl, Cl andDl. The multiplicative form of the canonical element for the quantum double is used to introduce the holomorphic coordinates on a general quantum dressing orbit. The coherent state is interpreted as a holomorphic function on this orbit with values in the carrier Hilbert space of an irreducible representation of the corresponding quantized enveloping algebra. Using Gauss decomposition, the commutation relations for the holomorphic coordinates on the dressing orbit are derived explicitly and given in a compactR-matrix formulation (generalizing this way theq-deformed Grassmann and flag manifolds). The antiholomorphic realization of the irreducible representations of a compact quantum group (the analogue of the Borel-Weil construction) is described using the concept of coherent state. The relation between representation theory and non-commutative differential geometry is suggested.
23 citations
TL;DR: In this article, the evolution of the field and the atom in the resonant two-photon Jaynes-Cummings model with the field initially in the coherent state is studied.
Abstract: The pure-state evolution of the atomic as well as the field states in the resonant two-photon Jaynes-Cummings model with the field initially in the coherent state is studied. Analytic expressions for various quantities involved are obtained under the large-n\ifmmode\bar\else\textasciimacron\fi{} approximation. It is shown that the atom as well as the field are approximately in the pure state for gt=k\ensuremath{\pi}/4, where k is an integer and in a completely pure state for gt=k\ensuremath{\pi}. The field states generated at the times gt=k\ensuremath{\pi}/4 are shown to be a quantum superposition of the coherent states for a particular choice of the relative phase. The interference between these states leads to a spiked photon-number distribution but the field is still Poissonian.
23 citations
TL;DR: In this paper, a set of N-dimensional functions, based on generalized SU(N)-symmetric coherent states, that represent finite-dimensional Wigner functions, Q-functions, and P-function are presented.
Abstract: We present a set of N-dimensional functions, based on generalized SU(N)-symmetric coherent states, that represent finite-dimensional Wigner functions, Q-functions, and P-functions. We then show the fundamental properties of these functions and discuss their usefulness for analyzing N-dimensional pure and mixed quantum states.
22 citations
TL;DR: In this article, the authors describe coherent states for a physical system governed by a Hamiltonian operator, in two-dimensional space, of spinless charged particles subject to a perpendicular magnetic field B, coupled with a harmonic potential.
22 citations
TL;DR: In this paper, the interference effects of the superposition of two classes of nonlinear coherent states, which are π 2 out of phase, were investigated numerically and numerically.
22 citations