Journal ArticleDOI
Some Mathematical Properties of Oscillator Phase Operators
TLDR
In this article, a general definition of cosine and sine operators for harmonic oscillator phase is proposed and its consequences examined, and an important feature of the spectral analysis is the ''chain sequence'' condition which ensures that C and S have unit norm.Abstract:
A general definition of ``cosine'' and ``sine'' operators, C and S, for harmonic oscillator phase is proposed and its consequences examined. An important feature of the spectral analysis is the ``chain sequence'' condition which ensures that C and S have unit norm. The (nonunitary) operator U = C + iS is shown to be an annihilation‐type operator whose spectral properties bear a remarkable analogy to those of the standard annihilation operator, although its spectrum fills the unit circle rather than the entire complex plane. Statistical properties of the eigenstates of U are discussed briefly.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.
Journal ArticleDOI
Phase properties of the quantized single-mode electromagnetic field.
David T. Pegg,Stephen M. Barnett +1 more
TL;DR: This paper investigates the properties of a Hermitian phase operator which follows directly and uniquely from the form of the phase states in this space and finds them to be well behaved.
Journal ArticleDOI
Converting Nonclassicality into Entanglement.
TL;DR: This work presents a general framework, based on superposition, for structurally connecting and converting nonclassicality to entanglement, and generalize and link convertibility properties from the resource theory of coherence, spin coherent states, and optical coherent states.
Journal ArticleDOI
Who is afraid of nonhermitian operators? A quantum description of angle and phase
TL;DR: In this article, the authors propose an unduly restricted framework for the theoretical description of quantum properties; non-hermitian operators, for instance unitary but also non-normal ones, may be acceptable as well if the projectors onto their eigenstates allow for a resolution of the identity operator, so as to preserve the probabilistic interpretation of the Hilbert space formalism.
References
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Journal ArticleDOI
Coherent and incoherent states of the radiation field
TL;DR: In this article, the photon statistics of arbitrary fields in fully quantum-mechanical terms are discussed, and a general method of representing the density operator for the field is discussed as well as a simple formulation of a superposition law for photon fields.
Book
Analytic Theory of Continued Fractions
TL;DR: In this article, a convergence theory of positive definite continued fractions is presented. But the convergence theory is not a generalization of the Stieltjes convergence theorem, and the convergence of continued fractions whose partial denominators are equal to unity is not discussed.
Journal ArticleDOI
Phase and Angle Variables in Quantum Mechanics
TL;DR: In this paper, a detailed analysis of the three-dimensional harmonic oscillator excited in coherent states is given, with special attention to the uncertainty relations and the transition to the classical limit.
Journal ArticleDOI
Quantum mechanical phase and time operator
TL;DR: In this paper, the phase operator for an oscillator is shown not to exist and a pair of non-commuting sin and cos operators are used to define uncertainty relations for phase and number.