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.

Approach of the continuous q-Hermite polynomials to x-representation of q-oscillator algebra and its coherent states

2019 ◽  
Vol 17 (02) ◽  
pp. 2050021
Author(s):  
H. Fakhri ◽  
S. E. Mousavi Gharalari
Keyword(s):  
Harmonic Oscillator ◽  
Generating Function ◽  
Coherent States ◽  
Finite Interval ◽  
Hermite Polynomials ◽  
Oscillator Algebra ◽  
Text Representation ◽  
Ladder Operators ◽  
Recursion Relations ◽  
Wilson Operator

We use the recursion relations of the continuous [Formula: see text]-Hermite polynomials and obtain the [Formula: see text]-difference realizations of the ladder operators of a [Formula: see text]-oscillator algebra in terms of the Askey–Wilson operator. For [Formula: see text]-deformed coherent states associated with a disc in the radius [Formula: see text], we obtain a compact form in [Formula: see text]-representation by using the generating function of the continuous [Formula: see text]-Hermite polynomials, too. In this way, we obtain a [Formula: see text]-difference realization for the [Formula: see text]-oscillator algebra in the finite interval [Formula: see text] as a [Formula: see text]-generalization of known differential formalism with respect to [Formula: see text] in the interval [Formula: see text] of the simple harmonic oscillator.

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.

NONCLASSICALITY AND DECOHERENCE OF PHOTON-ADDED THERMAL STATE

2010 ◽  
Vol 08 (08) ◽  
pp. 1373-1387 ◽  
Author(s):  
SHU-JING WANG ◽  
XUE-XIANG XU ◽  
SHAN-JUN MA
Keyword(s):  
Thermal State ◽  
Thermal Environment ◽  
Hermite Polynomials ◽  
Photon Number ◽  
Single Variable ◽  
State Characteristic ◽  
Number Formula ◽  
Analytical Expressions ◽  
Average Photon Number ◽  
Photon Number Distribution

Using the normally ordered form of thermal state characteristic of average photon number nc, we introduce the photon-added thermal state (PATS) and investigate its statistical properties, such as Mandel's Q-parameter, photon number distribution (PND), and Wigner function (WF). We then study its decoherence in a thermal environment with average thermal photon number [Formula: see text] and dissipative coefficient κ by deriving analytical expressions of the WF. The nonclassicality is discussed in terms of the negativity of the WF. It is found that the WF is always positive when [Formula: see text] for any number PATS. The expression for time evolution of the PND and the tomogram of PATS are also derived analytically, which are related to hypergeometric function and single variable Hermite polynomials.

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.

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.

PHOTON-NUMBER DISTRIBUTION AND WIGNER FUNCTION OF GENERALIZED PHOTON-MODULATED COHERENT STATE

2012 ◽  
Vol 27 (06) ◽  
pp. 1250013 ◽  
Author(s):  
JUN ZHOU ◽  
SHUAI WANG ◽  
JUN SONG ◽  
HONG-YI FAN
Keyword(s):  
Coherent State ◽  
Wigner Function ◽  
Hermite Polynomials ◽  
Photon Number ◽  
Single Variable ◽  
Normalization Factor ◽  
Nonclassical Properties ◽  
Number Distribution ◽  
Quantum Statistical ◽  
Photon Number Distribution

In this paper, we present the generalized photon-modulated coherent state (GPMCS) generated by repeatedly operating the combination of Bosonic creation and annihilation operators on the coherent state. It is found that the GPMCS is a Hermite-excited coherent state and its normalization factor is related to single-variable Hermite polynomials. Furthermore, some significant quantum statistical properties of the GPMCS are investigated, such as photon-number distribution (PND) and the Wigner function (WF). We find that the WF of the GPMCS has negative values when the generalized photon-modulation exists, which implies the nonclassical properties of the GPMCS.

scholarly journals Optimal time-resolved photon number distribution reconstruction of a cavity field by maximum likelihood

2012 ◽  
Vol 14 (11) ◽  
pp. 115007 ◽  
Author(s):  
C Sayrin ◽  
I Dotsenko ◽  
S Gleyzes ◽  
M Brune ◽  
J M Raimond ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Photon Number ◽  
Optimal Time ◽  
Cavity Field ◽  
Time Resolved ◽  
Number Distribution ◽  
Photon Number Distribution

SOME FEATURES OF SQUEEZED NEGATIVE BINOMIAL STATE

1992 ◽  
Vol 06 (03n04) ◽  
pp. 409-415 ◽  
Author(s):  
AMITABH JOSHI ◽  
S. V. LAWANDE
Keyword(s):  
Electromagnetic Field ◽  
Density Matrix ◽  
Wigner Function ◽  
Negative Binomial ◽  
Thermal State ◽  
Photon Number ◽  
Binomial State ◽  
Relationship Of ◽  
The Relationship ◽  
Photon Number Distribution

Properties of electromagnetic field in the squeezed negative binomial state are investigated in terms of photon number distribution and Wigner function. The relationship of the density matrix of the squeezed negative binomial state to the density matrix of the squeezed thermal state is shown explicitly. The possibility of generation of the negative binomial state is also discussed.

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