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Generalized intelligent states and squeezing
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In this paper, the Robertson-Schrodinger uncertainty relation for two observables A and B is shown to be minimized in the eigenstates of the operator λA+iB, λ being a complex number.Abstract:
The Robertson–Schrodinger uncertainty relation for two observables A and B is shown to be minimized in the eigenstates of the operator λA+iB, λ being a complex number. Such states, called generalized intelligent states (GIS), can exhibit arbitrarily strong squeezing of A or B. The time evolution of GIS is stable for Hamiltonians which admit linear in A and B invariants. Systems of GIS for the SU(1,1) and SU(2) groups are constructed and discussed. It is shown that SU(1,1) GIS contain all the Perelomov coherent states (CS) and the Barut and Girardello CS while the spin CS are a subset of SU(2) GIS. CS for an arbitrary semisimple Lie group can be considered as a GIS for the quadratures of the Weyl generators.read more
Citations
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'Nonclassical' states in quantum optics: a 'squeezed' review of the first 75 years
TL;DR: A review of studies performed in the field of non-classical states can be found in this article, with a focus on the evolution of Gaussian wave packets for an oscillator, a free particle and a particle moving in uniform constant electric and magnetic fields.
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Analytic representations in quantum mechanics
TL;DR: In this article, various Euclidean, hyperbolic and elliptic analytic representations of the harmonic oscillator are discussed and relations among them are discussed, and the general theory that relates the growth of analytic functions with the density of their zeros is applied to Bargmann functions and leads to theorems on the completeness of sequences of Glauber coherent states.
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SU(2) and SU(1,1) algebra Eigenstates: A Unified analytic approach to coherent and intelligent states
TL;DR: In this article, the concept of algebra eigenstates is introduced, which are defined for an arbitrary Lie group as eigen states of elements of the corresponding complex Lie algebra and applied to the SU(2) and SU(1,1) simple Lie groups.
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Analytic representations based on SU (1 , 1) coherent states and their applications
TL;DR: In this paper, a weak resolution of the identity in terms of the Perelomov SU(1,1) coherent states is presented which is valid even when the Bargmann index k is smaller than.
References
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Journal ArticleDOI
Two-photon coherent states of the radiation field
TL;DR: In this paper, the concept of two-photon coherent states is introduced for applications in quantum optics, which is a simple generalization of the well-known minimum-uncertainty wave packets.
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Coherent states: Theory and some Applications
TL;DR: In this article, a general algorithm for constructing coherent states of dynamical groups for a given quantum physical system is presented, and the result is that the coherent states are isomorphic to a coset space of group geometrical space.
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Squeezed spin states
Masahiro Kitagawa,Masahito Ueda +1 more
TL;DR: Two proposed mechanisms, referred to as one-axis twisting and two-axis countertwisting, are shown to reduce the standard quantum noise S/2 of the coherent S-spin state down to 1/2(S/3${)}^{1/3}$ and 1/3, respectively.
Journal ArticleDOI
Coherent states for arbitrary Lie group
TL;DR: In this paper, the concept of coherent states originally closely related to the nilpotent group of Weyl is generalized to arbitrary Lie groups and its features are investigated for the simplest Lie groups.
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Coherent states for arbitrary Lie group
TL;DR: In this article, the concept of coherent states originally closely related to the nilpotent group of Weyl is generalized to arbitrary Lie groups and its features are investigated for the simplest Lie groups.