Arik–Coon q-oscillator cat states on the noncommutative complex plane ℂq−1 and their nonclassical properties

2017 ◽  
Vol 14 (04) ◽  
pp. 1750060 ◽  
Author(s):  
H. Fakhri ◽  
M. Sayyah-Fard
Keyword(s):  
Complex Plane ◽  
Uncertainty Relation ◽  
Photon Statistics ◽  
Fock Representation ◽  
Nonclassical Properties ◽  
Resolution Of The Identity ◽  
Antibunching Effect ◽  
Cat States ◽  
Lowering Operator ◽  
Standard States

The normalized even and odd [Formula: see text]-cat states corresponding to Arik–Coon [Formula: see text]-oscillator on the noncommutative complex plane [Formula: see text] are constructed as the eigenstates of the lowering operator of a [Formula: see text]-deformed [Formula: see text] algebra with the left eigenvalues. We present the appropriate noncommutative measures in order to realize the resolution of the identity condition by the even and odd [Formula: see text]-cat states. Then, we obtain the [Formula: see text]-Bargmann–Fock realizations of the Fock representation of the [Formula: see text]-deformed [Formula: see text] algebra as well as the inner products of standard states in the [Formula: see text]-Bargmann representations of the even and odd subspaces. Also, the Euler’s formula of the [Formula: see text]-factorial and the Gaussian integrals based on the noncommutative [Formula: see text]-integration are obtained. Violation of the uncertainty relation, photon antibunching effect and sub-Poissonian photon statistics by the even and odd [Formula: see text]-cat states are considered in the cases [Formula: see text] and [Formula: see text].

Nonclassical properties of the Arik–Coon q−1-oscillator coherent states on the noncommutative complex plane ℂq

2017 ◽  
Vol 14 (11) ◽  
pp. 1750165 ◽  
Author(s):  
H. Fakhri ◽  
M. Sayyah-Fard
Keyword(s):  
Complex Plane ◽  
Coherent States ◽  
Uncertainty Relation ◽  
Photon Statistics ◽  
Squeezing Effect ◽  
Nonclassical Properties ◽  
Heisenberg’S Inequality ◽  
Photon Antibunching ◽  
Poissonian Statistics

This work has focused on the violation of uncertainty relation, squeezing effect, photon antibunching and sub-Poissonian statistics for the Arik–Coon [Formula: see text]-oscillator coherent states associated with the noncommutative complex plane [Formula: see text]. It is shown that one has to use a generalized definition for the covariance between the operators [Formula: see text] and [Formula: see text]. For [Formula: see text], Heisenberg's inequality violation with two different behaviors related to the role of the deformation parameter [Formula: see text] on the variances of the position and momentum operators is illustrated. We conclude that both weak and strong squeezing effects are exhibited by the [Formula: see text]-coherent states. In particular, strong squeezing effect is a direct consequent of the violation of Heisenberg's inequality. Moreover, the photon antibunching and sub-Poissonian photon statistics are two features of the [Formula: see text]-coherent states which are realized simultaneously with the squeezing effects. Clearly, the three later behaviors are different from their corresponding counterparts in the Arik–Coon [Formula: see text]-oscillator coherent states associated with a commutative complex plane.

Even and odd Wigner negative binomial states: Nonclassical properties

2015 ◽  
Vol 30 (37) ◽  
pp. 1550198 ◽  
Author(s):  
B. Mojaveri ◽  
A. Dehghani
Keyword(s):  
Negative Binomial ◽  
Heisenberg Algebra ◽  
Positive Definite ◽  
Fock Representation ◽  
Nonclassical Properties ◽  
Quadrature Squeezing ◽  
Mandel’S Parameter ◽  
Special Limit ◽  
Cat States ◽  
Poissonian Statistics

By using Wigner–Heisenberg algebra (WHA) and its Fock representation, even and odd Wigner negative binomial states (WNBSs) [Formula: see text] ([Formula: see text] corresponds to the ordinary even and odd negative binomial states (NBSs)) are introduced. These states can be reduced to the Wigner cat states in special limit. We establish the resolution of identity property for them through a positive definite measure on the unit disc. Some of their nonclassical properties, such as Mandel’s parameter and quadrature squeezing have been investigated numerically. We show that in contrast with the even NBSs, even WNBSs may exhibit sub-Poissonian statistics. Also squeezing in the field quadratures appears for both even and odd WNBSs. It is found that the deformation parameter [Formula: see text] plays an essential role in displaying highly nonclassical behaviors.

SUPERPOSITION OF THE λ-PARAMETERIZED SQUEEZED STATES

2000 ◽  
Vol 14 (07n08) ◽  
pp. 243-250
Author(s):  
XIAO-GUANG WANG ◽  
HONGCHEN FU
Keyword(s):  
Algebraic Characterization ◽  
Squeezed States ◽  
Nonclassical Properties ◽  
Intermediate States ◽  
Schrödinger Cat ◽  
Cat States ◽  
Superposition States

The superposition states of the λ-parameterized squeezed states are introduced and investigated. These states are intermediate states interpolating between the number and Schrödinger cat states and admit algebraic characterization in terms of su(1, 1) algebra. It is shown that these states exhibit remarkable nonclassical properties.

Photon added coherent states of the parity deformed oscillator

2019 ◽  
Vol 34 (14) ◽  
pp. 1950104 ◽  
Author(s):  
A. Dehghani ◽  
B. Mojaveri ◽  
S. Amiri Faseghandis
Keyword(s):  
Coherent States ◽  
Uncertainty Relation ◽  
Annihilation Operator ◽  
Single Mode ◽  
Heisenberg Algebra ◽  
Uncertainty Relations ◽  
Deformed Oscillator ◽  
Cat States ◽  
Poissonian Statistics ◽  
Creation Operators

Using the parity deformed Heisenberg algebra (RDHA), we first establish associated coherent states (RDCSs) for a pseudo-harmonic oscillator (PHO) system that are defined as eigenstates of a deformed annihilation operator. Such states can be expressed as superposition of an even and odd Wigner cat states.[Formula: see text] The RDCSs minimize a corresponding uncertainty relation, and resolve an identity condition through a positive definite measure which is explicitly derived. We introduce a class of single-mode excited coherent states (PARDCS) of the PHO through “m” times application of deformed creation operators to RDCS. For the states thus constructed, we analyze their statistical properties such as squeezing and sub-Poissonian statistics as well as their uncertainty relations.

Nonclassical properties of correlated two-mode Schrödinger cat states

1995 ◽  
Vol 51 (2) ◽  
pp. 1698-1701 ◽  
Author(s):  
Christopher C. Gerry ◽  
Rainer Grobe
Keyword(s):  
Nonclassical Properties ◽  
Schrödinger Cat ◽  
Cat States

Nonclassical properties and polarization degree of photon-subtracted entangled nonlinear coherent states

2019 ◽  
Vol 33 (21) ◽  
pp. 1950230 ◽  
Author(s):  
A. Dehghani ◽  
B. Mojaveri ◽  
M. Aryaie
Keyword(s):  
Coherent States ◽  
General Analysis ◽  
Degree Of Polarization ◽  
Polarization Degree ◽  
Photon Statistics ◽  
Quantum Mechanical ◽  
Entanglement Dynamics ◽  
Nonclassical Properties ◽  
Insight Into

As in two previous papers where nonclassical properties and entanglement dynamics were studied for entangled nonlinear coherent states (ENCS) [D. Afshar and A. Anbaraki, J. Opt. Soc. Am. B 33, 558 (2016).] and for photon-added entangled nonlinear coherent states (PAENCS) [A. Anbaraki, D. Afshar and M. Jafarpour, Eur. Phys. J. Plus 133, 2 (2018).], we study quantum mechanical treatments of photon-subtracted entangled nonlinear coherent states (PSENCS) introduced through applying annihilation operators on the ENCS, where the related nonlinearity functions are assumed to be harmonious. To gain insight into the effectiveness of photon subtracting from ENCS and comparing with the case already discussed as the PAENCS, we present a general analysis of nonclassical properties such as photon statistics and degree of polarization. We also derive the concurrence measure to quantify the entanglement of these states and look for conditions that provide information on whether they become maximally entangled. As a result, we can see that the photon depletion number m plays an important role in nonclassical effects. Especially, depending on whether the photon depletion number m is even or odd, one can observe different nonclassical effects.

scholarly journals ON A GENERAL FORMALISM OF NONLINEAR CHARGE COHERENT STATES, THEIR QUANTUM STATISTICS AND NONCLASSICAL PROPERTIES

2010 ◽  
Vol 25 (17) ◽  
pp. 3481-3504 ◽  
Author(s):  
F. EFTEKHARI ◽  
M. K. TAVASSOLY
Keyword(s):  
Coherent States ◽  
Nonclassical States ◽  
Mandel Parameter ◽  
Physical Systems ◽  
Nonclassical Properties ◽  
Deformed Algebra ◽  
Solvable Quantum ◽  
Antibunching Effect ◽  
Quantum Statistical ◽  
Special Case

In this paper, we will present a general formalism for constructing the nonlinear charge coherent states which in special case lead to the standard charge coherent states. The su Q(1, 1) algebra as a nonlinear deformed algebra realization of the introduced states is established. In addition, the corresponding even and odd nonlinear charge coherent states have also been introduced. The formalism has the potentiality to be applied to systems either with known "nonlinearity function" f(n) or solvable quantum system with known "discrete nondegenerate spectrum" en. As some physical appearances, a few known physical systems in the two mentioned categories have been considered. Finally, since the construction of nonclassical states is a central topic of quantum optics, nonclassical features and quantum statistical properties of the introduced states have been investigated by evaluating single- and two-mode squeezing, su (1, 1)-squeezing, Mandel parameter and antibunching effect (via g-correlation function) as well as some of their generalized forms we have introduced in the present paper.

Uniform operator σ-additivity of indefinite integrals induced by scalar-type spectral operators

1985 ◽  
Vol 101 (1-2) ◽  
pp. 141-146 ◽  
Author(s):  
S. Okada ◽  
W. Ricker
Keyword(s):  
Banach Space ◽  
Complex Plane ◽  
Borel Sets ◽  
Scalar Type ◽  
Resolution Of The Identity ◽  
Spectral Integral ◽  
Set Function

SynopsisThis note characterises those Banach space valued, scalar-type spectral operators T = ∫ z dP(z), where P is the resolution of the identity for T, whose indefinite spectral integral E→∫EzdP(z) as a set function of the Borel sets of the complex plane is countably additive with respect to the uniform operator topology.

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