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.

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 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.

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].

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.

Nonclassical properties and entanglement generation in an optical cavity containing two atomic Bose–Einstein condensates

2020 ◽  
Vol 34 (06) ◽  
pp. 2050075
Author(s):  
Ren-Fei Zheng ◽  
Qi-Hui Jiang ◽  
Lu Zhou ◽  
Wei-Ping Zhang
Keyword(s):  
Optical Cavity ◽  
Significant Loss ◽  
Cavity Field ◽  
Entanglement Generation ◽  
Field Coupling ◽  
Nonclassical Properties ◽  
Strong Atom ◽  
Collisional Interactions ◽  
Bose Einstein ◽  
Poissonian Statistics

We consider the model of a weakly driven optical cavity containing two clouds of atomic Bose–Einstein condensates (BECs). Nonclassical photon correlations and correlations between the two atomic BECs are investigated under different cavity conditions including strong atom-field coupling and bad cavity regime. We show that the nonlinear interatom collisional interactions in BEC leads to a significant loss of cavity light coherence. Various types of nonclassical properties are investigated such as sub-Poissonian statistics, antibunching and entanglement. We show that the entanglement can be generated between BECs and the cavity field. The time evolution of entanglement is also numerically studied.

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

Intrinsic decoherence effects on quantum dynamics of the nondegenerate two-photon f-deformed Jaynes–Cummings model governed by the Milburn equation

2007 ◽  
Vol 85 (10) ◽  
pp. 1071-1096 ◽  
Author(s):  
M H Naderi
Keyword(s):  
Quantum Dynamics ◽  
Cavity Field ◽  
Intrinsic Decoherence ◽  
Two Photon ◽  
Field Coupling ◽  
Nonclassical Properties ◽  
Quadrature Squeezing ◽  
Model Hamiltonian ◽  
Atomic Dipole ◽  
Atomic Population Inversion

In this paper, we study the influence of the intrinsic decoherence on quantum statistical properties of a generalized nonlinear interacting atom–field system, i.e., the nondegenerate two-photon f-deformed Jaynes–Cummings model governed by the Milburn equation. The model contains the nonlinearities of both the cavity–field and the atom–field coupling. Until now, very few exact solutions of nonlinear systems that include a form of decoherence have been presented. The main achievement of the present work is to find exact analytical solutions for the quantum dynamics of the nonlinear model under consideration in the presence of intrinsic decoherence. With the help of a supersymmetric transformation, we first put the model Hamiltonian into an appropriate form for treating the intrinsic decoherence. Then, by applying the superoperator technique, we find an exact solution of the Milburn equation for a nondegenerate two-photon f-deformed Jaynes–Cummings model. We use this solution to investigate the effects of the intrinsic decoherence on temporal evolution of various nonclassical properties of the system, i.e., atomic population inversion, atomic dipole squeezing, atom–field entanglement, sub-Poissonian photon statistics, cross correlation between the two modes and quadrature squeezing of the cavity field. Particularly, we compare the numerical results for three different cases of two-mode deformed, one-mode deformed, and nondeformed Jaynes–Cummings models. PACS Nos.: 42.50.Ct, 42.50.Dv, 03.65.Yz

Nonclassical properties and decoherence of fields in photon-added squeezing-enhanced thermal states

2014 ◽  
Vol 28 (19) ◽  
pp. 1450115 ◽  
Author(s):  
Zhen Wang ◽  
Xiang-guo Meng ◽  
Heng-mei Li ◽  
Hong-chun Yuan
Keyword(s):  
Thermal Noise ◽  
Photon Number ◽  
Sufficient Time ◽  
Thermal Photon ◽  
Time Interaction ◽  
Decoherence Time ◽  
Nonclassical Properties ◽  
Poissonian Statistics ◽  
Decoherence Effect ◽  
Thermal States

We put forward the photon-added squeezing-enhanced thermal states (PASETS) theoretically by adding photon to the squeezed enhancing thermal states (SETS) repeatedly. Based on the normally ordered density operator of PASETS, we investigate the nonclassical behavior of the PASETS by evaluating, both analytically and numerically, Mandel's Q-parameter, photon-number distribution (PND), and Wigner function (WF). It is found that smaller squeezing parameter r and thermal photon number nc can lead to more chance of the appearance of sub-Poissonian statistics. And it is shown that the PND of PASETS exhibit more remarkable oscillations than that of SETS in stronger squeezing case. The WF exhibit partial negativity in phase space and the squeezing parameter r can result in both squeezing and rotating effect. By investigating the fidelity between PASETS and SETS shows that the fidelity tender to steady values in the high value of squeezing parameter or thermal photon number. In addition, the decoherence effect on the PASETS is examined by the time-evolution of the analytical WF in thermal channel. The results show that the PASETS shall lose nonclassicality and non-Gaussianity and reduce to classical states with Gaussian distribution after sufficient time interaction with the thermal noise. And larger photon-added number or thermal photon number shall render shorter decoherence time.

ON THE GENERATION OF INTERMEDIATE NUMBER SQUEEZED STATE OF THE QUANTIZED RADIATION FIELD

1996 ◽  
Vol 10 (14) ◽  
pp. 671-678 ◽  
Author(s):  
B. BASEIA ◽  
A.F. DE LIMA ◽  
V.S. BAGNATO
Keyword(s):  
Radiation Field ◽  
Slight Modification ◽  
Squeezed State ◽  
Nonclassical Properties ◽  
Number State ◽  
Previous Definition ◽  
Quantized Radiation Field ◽  
Poissonian Statistics

Recently, a new state of the quantized radiation field — the intermediate number squeezed state (INSS) — has been introduced in the literature: it interpolates between the number state |n> and the squeezed state |z, α>=Ŝ(z)|α>, and exhibits interesting nonclassical properties as antibunching, sub-Poissonian statistics and squeezing. Here we introduce a slight modification in the previous definition allowing us a proposal to generate the INSS. Nonclassical properties using a new set of parameters are also studied.

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