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.

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].

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 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.

Nonclassical Properties of the Even and Odd Intermediate Number Squeezed States

1998 ◽  
Vol 12 (01) ◽  
pp. 23-33 ◽  
Author(s):  
B. Roy
Keyword(s):  
Coherent States ◽  
Squeezed States ◽  
Nonclassical Properties ◽  
Quadrature Squeezing ◽  
Poissonian Statistics

The even and odd intermediate number squeezed states are introduced. These states reduce to even (odd) number states and even (odd) squeezed coherent states in different limits. It is shown that these states exhibit nonclassical effects such as sub (super) Poissonian statistics, quadrature squeezing, antibunching for certain ranges of the parameters involved.

Superposition of single-mode para-Bose coherent states: Generation and nonclassical properties

2018 ◽  
Vol 33 (22) ◽  
pp. 1850134 ◽  
Author(s):  
B. Mojaveri ◽  
A. Dehghani ◽  
R. Jafarzadeh Bahrbeig
Keyword(s):  
Coherent States ◽  
Essential Role ◽  
Relative Phase ◽  
Single Mode ◽  
State Distribution ◽  
Simple Scheme ◽  
Nonclassical Properties ◽  
Deformation Parameters ◽  
Fock State

In this paper, we introduce two classes of superposed states generated by a superposition of two single-mode para-Bose coherent states (CS) with arbitrary relative phase factors. The first class is superposition of two opposite para-Bose CS and second class consists of two para-Bose CS, [Formula: see text] out of phase with each other. These states are reduced to the well-known superposed single-mode CS of the simple harmonic oscillator when the deformation parameter tends to one. We study the nonclassical properties of the introduced states by evaluating their para-Bose Fock state distribution, second-order squeezing, Klyshko’s and Mandel’s parameters. We investigate the essential role of coherent and deformation parameters on their nonclassicality. We show that some nonclassical properties of these states are different from those of the even and odd coherent states. Finally, we present a simple scheme for the physical generation of the introduced states.

Even and odd coherent states of supersymmetric harmonic oscillators and their nonclassical properties

2016 ◽  
Vol 30 (07) ◽  
pp. 1650026 ◽  
Author(s):  
Davood Afshar ◽  
Amin Motamedinasab ◽  
Azam Anbaraki ◽  
Mojtaba Jafarpour
Keyword(s):  
Harmonic Oscillator ◽  
Coherent States ◽  
Bell States ◽  
Harmonic Oscillators ◽  
Nonclassical Properties ◽  
Logical Qubits ◽  
Poissonian Statistics

In this paper, we have constructed even and odd superpositions of supercoherent states, similar to the standard even and odd coherent states of the harmonic oscillator. Then, their nonclassical properties, that is, squeezing and entanglement have been studied. We have observed that even supercoherent states show squeezing behavior for some values of parameters involved, while odd supercoherent states do not show squeezing at all. Also sub-Poissonian statistics have been observed for some ranges of the parameters in both states. We have also shown that these states may be considered as logical qubits which reduce to the Bell states at a limit, with concurrence equal to 1.

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