SUPERPOSITIONS OF SQUEEZED COHERENT STATES: PROPERTIES AND GENERATION

1999 ◽  
Vol 13 (17) ◽  
pp. 2299-2312 ◽  
Author(s):  
A.-S. F. OBADA ◽  
G. M. ABD AL-KADER
Keyword(s):  
Distribution Function ◽  
Phase Space ◽  
Coherent States ◽  
Phase Distribution ◽  
Coherence Function ◽  
Photon Number ◽  
Distribution Functions ◽  
Numerical Results ◽  
Quadrature Component ◽  
Photon Number Distribution

The s-parameterized charactristic function for the superposition of squeezed coherent states (SCS's) is given. The s-parameterized distribution functions for the superposition of SCS's are investigated. Various moments are calculated by using this charactristic function. The Glauber second-order coherence function is calculated. The photon number distribution of the superposition of SCS's studied. Analytical and numerical results for the quadrature component distributions for the superposition of a pair of SCS's are presented. The phase distribution calculated from the integration of s-parameterized distribution function over the phase space. A generation scheme is discussed.

Nonclassicality of photon-modulated spin coherent states in the Holstein-Primakoff realization

2021 ◽  
Author(s):  
Xiaoyan Zhang ◽  
Jisuo Wang ◽  
Lei Wang ◽  
Xiangguo Meng ◽  
Baolong Liang
Keyword(s):  
Coherent States ◽  
Wigner Distribution ◽  
Hermite Polynomials ◽  
Photon Number ◽  
Spin Ladder ◽  
Bernoulli Distribution ◽  
Ladder Operators ◽  
Spin Number ◽  
Photon Number Distribution ◽  
Spin Coherent States

Abstract Two new photon-modulated spin coherent states (SCSs) are introduced by operating the spin ladder operators J ± on the ordinary SCS in the Holstein-Primakoff realization and the nonclassicality is exhibited via their photon number distribution, second-order correlation function, photocount distribution and negativity of Wigner distribution. Analytical results show that the photocount distribution is a Bernoulli distribution and the Wigner functions are only associated with two-variable Hermite polynomials. Compared with the ordinary SCS, the photon-modulated SCSs exhibit more stronger nonclassicality in certain regions of the photon modulated number k and spin number j, which means that the nonclassicality can be enhanced by selecting suitable parameters.

On the Squeezing and Displacement of nth-Order

1997 ◽  
Vol 11 (09n10) ◽  
pp. 399-406
Author(s):  
Norton G. de Almeida ◽  
Célia M. A. Dantas
Keyword(s):  
Coherent State ◽  
Coherent States ◽  
Photon Number ◽  
Natural Generalization ◽  
Statistical Properties ◽  
Number Distribution ◽  
Quantum Statistical ◽  
Photon Number Distribution

The norder expressions for the squeezed and coherent states are derived as a natural generalization of the usual squeezed coherent and coherent states. The photon number distribution of n order of squeezed coherent states that are eigenstates of the operators [Formula: see text] is derived. The n order coherent state is a particular case of the states that we are now deriving. Some mathematical and quantum statistical properties of these states are discussed.

GENERALIZED SUPERPOSITIONS OF SQUEEZED COHERENT STATES

2001 ◽  
Vol 15 (27) ◽  
pp. 1265-1270
Author(s):  
G. M. ABD AL-KADER
Keyword(s):  
Characteristic Function ◽  
Coherent States ◽  
Photon Number ◽  
Number Distribution ◽  
Q Function ◽  
Photon Number Distribution

The superpositions of a pair of squeezed coherent states (SCS) with different squeezing parameters are defined. The characteristic function (CF) for the generalized superpositions of SCSs is given. Photon number distribution for these states is considered. The Q-function for the generalized superposition of SCSs is investigated.

INFLUENCE OF SQUEEZING OPERATOR ON THE QUANTUM PROPERTIES OF VARIOUS BINOMIAL STATES

2001 ◽  
Vol 15 (01) ◽  
pp. 75-100 ◽  
Author(s):  
FAISAL A. A. EL-ORANY ◽  
M. SEBAWE ABDALLA ◽  
A-.S. F. OBADA ◽  
G. M. ABD AL-KADER
Keyword(s):  
Distribution Function ◽  
Correlation Function ◽  
Phase Distribution ◽  
Single Mode ◽  
Second Order ◽  
Distribution Functions ◽  
Quantum Properties ◽  
Quadrature Phase ◽  
Squeezing Operator ◽  
Quasiprobability Distribution

In this communication we investigate the action of a single-mode squeeze operator on the statistical behaviour of different binomial states. For the resulting states (squeezed generalized binomial states) normalized second-order correlation function, quasiprobability distribution functions and the distribution function P(x) associated with the quadrature x are studied both analytically and numerically. Furthermore, the quadrature phase distribution as well as the phase distribution in the framework of Pegg–Barnett formalism are discussed.

Orbit Tomography of energetic particle distribution functions

2021 ◽  
Author(s):  
Luke Stagner ◽  
William W Heidbrink ◽  
Mirko Salewski ◽  
Asger Schou Jacobsen ◽  
Benedikt Geiger
Keyword(s):  
Distribution Function ◽  
Phase Space ◽  
Energetic Particle ◽  
Particle Distribution ◽  
Distribution Functions ◽  
Velocity Space ◽  
Space Distribution ◽  
Weight Functions ◽  
Ion Distribution ◽  
Fast Ions

Abstract Both fast ions and runaway electrons are described by distribution functions, the understanding of which are of critical importance for the success of future fusion devices such as ITER. Typically, energetic particle diagnostics are only sensitive to a limited subsection of the energetic particle phase-space which is often insufficient for model validation. However, previous publications show that multiple measurements of a single spatially localized volume can be used to reconstruct a distribution function of the energetic particle velocity-space by using the diagnostics' velocity-space weight functions, i.e. Velocity-space Tomography. In this work we use the recently formulated orbit weight functions to remove the restriction of spatially localized measurements and present Orbit Tomography, which is used to reconstruct the 3D phase-space distribution of all energetic particle orbits in the plasma. Through a transformation of the orbit distribution, the full energetic particle distribution function can be determined in the standard {energy,pitch,r,z}-space. We benchmark the technique by reconstructing the fast-ion distribution function of an MHD-quiescent DIII-D discharge using synthetic and experimental FIDA measurements. We also use the method to study the redistribution of fast ions during a sawtooth crash at ASDEX Upgrade using FIDA measurements. Finally, a comparison between the Orbit Tomography and Velocity-space Tomography is shown.

DYNAMICS OF A NONDEGENERATE TWO-PHOTON JAYNES–CUMMINGS MODEL

1995 ◽  
Vol 09 (11n12) ◽  
pp. 665-683 ◽  
Author(s):  
RICHARD D'SOUZA ◽  
ARUNDHATI S. JAYARAO
Keyword(s):  
Coherent States ◽  
Coherence Function ◽  
Dynamical Behavior ◽  
Photon Number ◽  
Stark Shift ◽  
Atomic Inversion ◽  
Two Photon ◽  
Different Types ◽  
Atomic Squeezing ◽  
Average Photon Number

A generalized Jaynes–Cummings model including the Stark shifts is investigated where the transition is mediated by two different modes of photons. For two different types of correlated field states, the pair coherent states and two-mode SU(1, 1) coherent states, the effect of including the Stark shift on the dynamical behavior of atomic inversion, atomic squeezing parameters, second order coherence function, and photon number distribution is investigated. Our results indicate significant changes in the behavior of these quantities for large and small average photon number <n> in the presence and absence of Stark shift and depending on the type of correlated field involved.

Distribution functions for resonantly trapped orbits in our Galaxy

2017 ◽  
Vol 13 (S334) ◽  
pp. 341-342
Author(s):  
G. Monari ◽  
B. Famaey ◽  
J.-B. Fouvry ◽  
J. Binney
Keyword(s):  
Distribution Function ◽  
Phase Space ◽  
Stellar Population ◽  
Distribution Functions ◽  
Space Distribution ◽  
Galactic Disc ◽  
Phase Mixing ◽  
Phase Space Distribution ◽  
Resonant Region ◽  
Time Average

AbstractWe show how to capture the behaviour of the phase-space distribution function (DF) of a Galactic disc stellar population at a resonance. This is done by averaging the Hamiltonian over fast angle variables and re-expressing the DF in terms of a new set of canonical actions and angles variables valid in the resonant region. We then assign to the resonant DF the time average along the orbits of the axisymmetric DF expressed in the new set of actions and angles. This boils down to phase-mixing the DF in terms of the new angles, such that the DF for trapped orbits only depends on the new set of actions. This opens the way to quantitatively fitting the effects of the bar and spirals to Gaia data in terms of distribution functions in action space.

scholarly journals Maximally Entangled SU(1,1) Semi Coherent States

2021 ◽  
Author(s):  
A.-S. F. Obada ◽  
M. M. A. Ahmed ◽  
Hoda A. Ali ◽  
Somia Abd-Elnabi ◽  
S. Sanad
Keyword(s):  
Distribution Function ◽  
Correlation Function ◽  
Probability Distribution Function ◽  
Coherent States ◽  
Distribution Functions ◽  
Entangled States ◽  
Nonclassical Properties ◽  
Quadrature Squeezing ◽  
Maximally Entangled States ◽  
Quasiprobability Distribution

AbstractIn this paper, we consider a special type of maximally entangled states namely by entangled SU(1,1) semi coherent states by using SU(1,1) semi coherent states(SU(1,1) Semi CS). The entanglement characteristics of these entangled states are studied by evaluating the concurrence.We investigate some of their nonclassical properties,especially probability distribution function,second-order correlation function and quadrature squeezing . Further, the quasiprobability distribution functions (Q-functions) is discussed.

Scaling

2018 ◽  
Author(s):  
Stefan Thurner ◽  
Rudolf Hanel ◽  
Peter Klimekl
Keyword(s):  
Distribution Function ◽  
Dynamical Systems ◽  
Complex Systems ◽  
Power Law ◽  
Scaling Laws ◽  
Power Laws ◽  
Distribution Functions ◽  
Temporal Process ◽  
Approximate Power

Scaling appears practically everywhere in science; it basically quantifies how the properties or shapes of an object change with the scale of the object. Scaling laws are always associated with power laws. The scaling object can be a function, a structure, a physical law, or a distribution function that describes the statistics of a system or a temporal process. We focus on scaling laws that appear in the statistical description of stochastic complex systems, where scaling appears in the distribution functions of observable quantities of dynamical systems or processes. The distribution functions exhibit power laws, approximate power laws, or fat-tailed distributions. Understanding their origin and how power law exponents can be related to the particular nature of a system, is one of the aims of the book.We comment on fitting power laws.

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