New approach to generating functions of single- and two-variable even- and odd-Hermite polynomials and applications in quantum optics

2014 ◽  
Vol 28 (32) ◽  
pp. 1450249 ◽  
Author(s):  
Fang Jia ◽  
Shuang Xu ◽  
Li-Yun Hu ◽  
Zhenglu Duan ◽  
Jie-Hui Huang
Keyword(s):  
Quantum Optics ◽  
Generating Functions ◽  
Coherent States ◽  
Hermite Polynomials ◽  
Quantum States ◽  
Iwop Technique ◽  
New Approach ◽  
The Iwop Technique ◽  
New Formula ◽  
Entangled Coherent States

Using the IWOP technique and completeness of representation, we obtain the integral expressions of single- and two-variable Hermite polynomials. Based on this, we further derive the generating functions of single- and two-variable even- and odd-Hermit polynomials. This method seems more concise and direct. In addition, some applications such as deriving new formula and constructing new two-mode quantum states are discussed. It is found that two-variable Hermite polynomials excitation can used to produce entangled coherent states.

scholarly journals CONTRADICTION TO THE TABLE OF D. I. MENDELEEV AND THEIR ELIMINATION

2021 ◽  
Vol 2 (446) ◽  
pp. 14-21
Author(s):  
N.К. Akhmetov ◽  
G.U. Ilyasova ◽  
S. K. Kazybekova
Keyword(s):  
Quantum Number ◽  
Periodic Table ◽  
Chemical Elements ◽  
Principal Quantum Number ◽  
Quantum States ◽  
Outer Electron ◽  
New Approach ◽  
Electronic Configurations ◽  
New Formula ◽  
Electron Shells

The article discusses a new approach to the formation of periods of the Periodic Table of Mendeleev. With the help of the new formula and the first proposed quantum states of the outer electron shells of atoms of chemical elements, the periods of the periodic table are reformatted. It is supposed to reduce the number of periods in the table by introducing the corresponding sub-periods. This is confirmed by the material given in the article. The following description of the order of formation of electron layers is proposed: the principal quantum number (n), then the newly proposed quantum states of electrons («first» and «second»), which in turn constitute the electronic configurations of sub-periods in periods, and only then the remaining quantum orbitals (s, p, d and f).

NEW APPROACH FOR FINDING MULTIPARTITE ENTANGLED STATE REPRESENTATIONS VIA THE IWOP TECHNIQUE

2007 ◽  
Vol 22 (24) ◽  
pp. 4481-4494 ◽  
Author(s):  
HONG-YI FAN ◽  
SHU-GUANG LIU
Keyword(s):  
Entangled State ◽  
Iwop Technique ◽  
Entangled State Representation ◽  
Completeness Relation ◽  
State Representation ◽  
Gaussian Form ◽  
New Approach ◽  
The Iwop Technique ◽  
Multipartite Entangled State

We present a new approach to finding multipartite entangled state representation by decomposing normally ordered Gaussian-form operator in completeness relation, the technique of integration within an ordered product (IWOP) of operators is essential in this searching.

ENTANGLED STATES, SQUEEZED STATES GAINED VIA THE ROUTE OF DEVELOPING DIRAC'S SYMBOLIC METHOD AND THEIR APPLICATIONS

2004 ◽  
Vol 18 (10n11) ◽  
pp. 1387-1455 ◽  
Author(s):  
HONG-YI FAN
Keyword(s):  
Quantum Optics ◽  
Fourier Optics ◽  
Entangled States ◽  
Entangled State ◽  
Squeezed States ◽  
Iwop Technique ◽  
The Iwop Technique ◽  
Operator Ordering ◽  
Symbolic Method ◽  
Interdisciplinary Study

Via the route of developing Dirac's symbolic method by virtue of the technique of integration within an ordered product (IWOP) of operators we derive various entangled state representations, squeezed states, and operator ordering formulae. We show how the entangled states can be applied to many aspects of quantum optics theory. The applications of the entangled states in the interdisciplinary study of quantum optics and Fourier optics are also introduced. All these discussions exhibit the power of Dirac's symbolic method with the aid of the IWOP technique.

ABCD rule for Gaussian beam propagation in the context of quantum optics derived by the IWOP technique

2006 ◽  
Vol 321 (9) ◽  
pp. 2116-2127 ◽  
Author(s):  
Hong-yi Fan ◽  
Hai-liang Lu ◽  
Wei-bo Gao ◽  
Xue-fen Xu
Keyword(s):  
Quantum Optics ◽  
Gaussian Beam ◽  
Beam Propagation ◽  
Iwop Technique ◽  
The Iwop Technique ◽  
Abcd Rule

New Approach to the Theory of Circular Dichroism

1998 ◽  
Vol 63 (8) ◽  
pp. 1187-1201 ◽  
Author(s):  
Jaroslav Zamastil ◽  
Lubomír Skála ◽  
Petr Pančoška ◽  
Oldřich Bílek
Keyword(s):  
Electromagnetic Wave ◽  
Circular Dichroism ◽  
Electromagnetic Waves ◽  
Maxwell Equations ◽  
Optically Active ◽  
Semiclassical Approach ◽  
New Approach ◽  
Isotropic Media ◽  
New Formula ◽  
Circular Dichroïsm

Using the semiclassical approach for the description of the propagation of the electromagnetic waves in optically active isotropic media we derive a new formula for the circular dichroism parameter. The theory is based on the idea of the time damped electromagnetic wave interacting with the molecules of the sample. In this theory, the Lambert-Beer law need not be taken as an empirical law, however, it follows naturally from the requirement that the electromagnetic wave obeys the Maxwell equations.

Quantum optics with nitrogen-vacancy centres in diamond

2017 ◽  
Author(s):  
Yiwen Chu ◽  
Mikhail D. Lukin
Keyword(s):  
Optical Properties ◽  
Quantum Information ◽  
Solid State ◽  
Quantum Optics ◽  
Quantum States ◽  
Nitrogen Vacancy ◽  
Common Theme ◽  
External Effects ◽  
Promising Candidate ◽  
Optical Photons

A common theme in the implementation of quantum technologies involves addressing the seemingly contradictory needs for controllability and isolation from external effects. Undesirable effects of the environment must be minimized, while at the same time techniques and tools must be developed that enable interaction with the system in a controllable and well-defined manner. This chapter addresses several aspects of this theme with regard to a particularly promising candidate for developing applications in both metrology and quantum information, namely the nitrogen-vacancy (NV) centre in diamond. The chapter describes how the quantum states of NV centres can be manipulated, probed, and efficiently coupled with optical photons. It also discusses ways of tackling the challenges of controlling the optical properties of these emitters inside a complex solid state environment.

scholarly journals Bipartite quantum channels using multipartite cluster-type entangled coherent states

2010 ◽  
Vol 81 (4) ◽  
Author(s):  
P. P. Munhoz ◽  
J. A. Roversi ◽  
A. Vidiella-Barranco ◽  
F. L. Semião
Keyword(s):  
Coherent States ◽  
Quantum Channels ◽  
Cluster Type ◽  
Entangled Coherent States

SEPARABILITY: A NEW APPROACH FROM THE CONIC STRUCTURE OF POSITIVE OPERATORS

2011 ◽  
Vol 09 (supp01) ◽  
pp. 415-422
Author(s):  
D. SALGADO ◽  
J. L. SÁNCHEZ-GÓMEZ ◽  
M. FERRERO
Keyword(s):  
Pure State ◽  
Convex Combination ◽  
Quantum States ◽  
Necessary Condition ◽  
New Approach ◽  
Product Matrix ◽  
Separability Problem ◽  
Multipartite System ◽  
Arbitrary Dimensions ◽  
Bipartite Case

We exploit the cone structure of unnormalized quantum states to reformulate the separability problem. Firstly a convex combination of every quantum state ρ in terms of a state Cρ with the same rank and another one Eρ with lower rank is perfomed, with weights 1 − λρ and λρ, respectively. Secondly a scalar [Formula: see text] is computed. Then ρ is separable if, and only if, [Formula: see text]. The computation of [Formula: see text] has been undergone under the simplest choice for Cρ as a product matrix and Eρ being a pure state, valid for any bipartite and multipartite system in arbitrary dimensions. A necessary condition is also formulated when Eρ is not pure in the bipartite case.

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