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.

Nonlinear time evolution of coherent states with observation of super revivals in a generalized isotonic oscillator

2014 ◽  
Vol 11 (04) ◽  
pp. 1450027
Author(s):  
V. Chithiika Ruby ◽  
P. Muruganandam ◽  
M. Senthilvelan
Keyword(s):  
Energy Spectrum ◽  
Time Evolution ◽  
Coherent States ◽  
Uncertainty Relation ◽  
Cubic Nonlinearity ◽  
Expectation Values ◽  
Ladder Operators ◽  
Deformed Oscillator ◽  
Fractional Revivals ◽  
Nonlinear Energy

In this paper, we investigate revival and super revivals of nonlinear coherent states while generating these states through the interaction of coherent states of a generalized isotonic oscillator with the nonlinear media during time evolution. We construct the f-deformed generalized isotonic oscillator which is a non-isochronous partner of the generalized isotonic oscillator. We connect these two nonlinear oscillators through deformed ladder operators. The generalized isotonic oscillator possesses linear energy spectrum whereas f-deformed generalized isotonic oscillator exhibits nonlinear energy spectrum. The presence of the cubic nonlinearity in the f-deformed oscillator motivates us to study revivals, super and fractional revivals of coherent states which are nonlinearly evolved. We also investigate time-dependent expectation values of uncertainties in certain canonically conjugate variables and demonstrate that at revival and super revival times the uncertainty relation attains its minimum value.

UNCERTAINTY RELATIONS FOR THE TIME-DEPENDENT SINGULAR OSCILLATOR

2006 ◽  
Vol 20 (10) ◽  
pp. 1211-1231 ◽  
Author(s):  
J. R. CHOI ◽  
I. H. NAHM
Keyword(s):  
Harmonic Oscillator ◽  
Excited States ◽  
Ground State ◽  
Coherent States ◽  
System Approach ◽  
Uncertainty Relation ◽  
Time Dependent ◽  
Uncertainty Relations ◽  
Number State ◽  
State Uncertainty

Uncertainty relations for the time-dependent singular oscillator in the number state and in the coherent state are investigated. We applied our developement to the Caldirola–Kanai oscillator perturbed by a singularity. For this system, the variation (Δx) decreased exponentially while (Δp) increased exponentially with time both in the number and in the coherent states. As k → 0 and χ → 0, the number state uncertainty relation in the ground state becomes 0.583216ℏ which is somewhat larger than that of the standard harmonic oscillator, ℏ/2. On the other hand, the uncertainty relation in all excited states become smaller than that of the standard harmonic oscillator with the same quantum number n. However, as k → ∞ and χ → 0, the uncertainty relations of the system approach the uncertainty relations of the standard harmonic oscillator, (n+1/2)ℏ.

scholarly journals DYNAMICS OF STATES IN THE NONLINEAR INTERACTION REGIME BETWEEN A THREE-LEVEL ATOM AND GENERALIZED COHERENT STATES AND THEIR NON-CLASSICAL FEATURES

2012 ◽  
Vol 26 (05) ◽  
pp. 1250027 ◽  
Author(s):  
M. K. TAVASSOLY ◽  
F. YADOLLAHI
Keyword(s):  
Coherent State ◽  
Coherent States ◽  
Exact Analytical Solution ◽  
Photon Number ◽  
Single Mode ◽  
Level Atom ◽  
Special Cases ◽  
Interaction Regime ◽  
Atomic Population Inversion ◽  
Poissonian Statistics

The present study investigates the interaction of an equidistant three-level atom and a single-mode cavity field that has been initially prepared in a generalized coherent state. The atom–field interaction is considered to be, in general, intensity-dependent. We suppose that the nonlinearity of the initial generalized coherent state of the field and the intensity-dependent coupling between atom and field are distinctly chosen. Interestingly, an exact analytical solution for the time evolution of the state of atom–field system can be found in this general regime in terms of the nonlinearity functions. Finally, the presented formalism has been applied to a few known physical systems such as Gilmore–Perelomov and Barut–Girardello coherent states of SU(1,1) group, as well as a few special cases of interest. Mean photon number and atomic population inversion will be calculated, in addition to investigating particular non-classicality features such as revivals, sub-Poissonian statistics and quadratures squeezing of the obtained states of the entire system. Also, our results will be compared with some of the earlier works in this particular subject.

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.

Noncommutative photon-added squeezed vacuum states

2020 ◽  
Vol 35 (20) ◽  
pp. 2050167 ◽  
Author(s):  
H. Fakhri ◽  
M. Sayyah-Fard
Keyword(s):  
Annihilation Operator ◽  
Single Mode ◽  
Noise Band ◽  
Two Photon ◽  
Squeezed Vacuum ◽  
Quadrature Squeezing ◽  
Vacuum States ◽  
Poissonian Statistics ◽  
Photon Annihilation

Noncommutative optical squeezed vacuum states are constructed as eigenstates of an appropriate two-photon annihilation operator corresponding to the Biedenharn–Macfarlane [Formula: see text]-oscillator. We consider in details the role of noncommutativity parameter [Formula: see text] on the nonclassical behaviors including quadrature squeezing and sub-Poissonian statistics. Also, we construct the noncommutative photon-added squeezed vacuum states and consider their Hillery-type higher-order squeezing and single-mode noise band.

UNCERTAINTY RELATIONS FOR A DEFORMED OSCILLATOR

2006 ◽  
Vol 20 (11n13) ◽  
pp. 1851-1859 ◽  
Author(s):  
JOSÉ RÉCAMIER ◽  
W. LUIS MOCHÁN ◽  
MARÍA GORAYEB ◽  
JOSÉ L. PAZ ◽  
ROCÍO JÁUREGUI
Keyword(s):  
Coherent States ◽  
Morse Potential ◽  
Temporal Evolution ◽  
Energy Spectra ◽  
Uncertainty Relations ◽  
Morse Oscillator ◽  
Algebraic Representation ◽  
Creation And Annihilation Operators ◽  
Deformed Oscillator ◽  
Minimum Uncertainty

We construct a deformed oscillator whose energy spectra is similar to that of a Morse potential. We obtain a convenient algebraic representation of the displacement and the momentum of a Morse oscillator by expanding them in terms of deformed creation and annihilation operators and we compute their average values between approximate coherent states of the deformed oscillator, and we compare them to the results obtained using the exact Morse coordinate and momenta. Finally we evaluate the temporal evolution of the dispersion (Δx)(Δp) and show that these states are not minimum uncertainty states.

DEFORMED HARMONIC OSCILLATOR FOR NON-HERMITIAN OPERATOR AND THE BEHAVIOR OF PT AND CPT SYMMETRIES

2006 ◽  
Vol 20 (16) ◽  
pp. 2313-2322 ◽  
Author(s):  
A. JANNUSSIS ◽  
K. VLACHOS ◽  
V. PAPATHEOU ◽  
A. STREKLAS
Keyword(s):  
Harmonic Oscillator ◽  
Coherent States ◽  
Hermitian Operator ◽  
Uncertainty Relations ◽  
Complex Spectrum ◽  
Cpt Symmetry ◽  
Solid State Physics ◽  
Special Values ◽  
Deformed Oscillator ◽  
Positive Spectrum

In the present paper we study the deformed harmonic oscillator for the non-Hermitian operator [Formula: see text] where λ,θ are real positive parameters, since the parameters α,β,m are for the general case complex. For the case α=1,β=1 and mass m real, we find the eigenfunctions and eigenvalues of energy, the coherent states, the time evolution of the operators [Formula: see text] in the Heisenberg picture and the uncertainty relations. In this case the operator ℋ is Hermitian and PT-symmetric. Also for the case m complex α=1,β=1, the operator ℋ is non-Hermitian and no more PT symmetric, but CPT symmetric with real discrete positive spectrum and the CPT symmetry is preserved. In the general case α,β,m complex, for the non-Hermitian operator ℋ, we obtain complex spectrum and for the special values of the complex parameters α,β the spectrum is real discrete and positive and the CPT symmetry is preserved. The general problem of deformed oscillator for non hermitian operators can be applied to the Solid State Physics.

Some aspects of a weak Weyl–Heisenberg algebra deformation

2005 ◽  
Vol 83 (9) ◽  
pp. 929-939
Author(s):  
N Boucerredj ◽  
N Mebarki ◽  
A Benslama
Keyword(s):  
Wave Function ◽  
Coherent States ◽  
Deformation Parameter ◽  
Annihilation Operator ◽  
Heisenberg Algebra ◽  
Integral Approach ◽  
Displacement Operator ◽  
Fock Representation ◽  
Generalized Coherent States ◽  
Simple Formalism

In the weak deformation (WD) approximation of the Weyl–Heisenberg algebra, the corresponding generalized coherent states and displacement operator are constructed. It is shown that those states, and contrary to the non-deformed Weyl-Heisenberg algebra, are not eigenstates of the annihilation operator. Moreover, and as an alternative to the Chaïchian et al. Q-deformed path integral approach (where Q is the deformation parameter), using the Bargmann Fock representation, we propose in the WD approximation, a general simple formalism. As an application, we calculate the propagator and the wave function of the harmonic oscillator.PACS Nos.: 03.65.Fd, 31.15.Kb

ON q-DEFORMED PARA OSCILLATORS AND PARA-q OSCILLATORS

1992 ◽  
Vol 07 (28) ◽  
pp. 2593-2600 ◽  
Author(s):  
M. KRISHNA KUMARI ◽  
P. SHANTA ◽  
S. CHATURVEDI ◽  
V. SRINIVASAN
Keyword(s):  
Harmonic Oscillator ◽  
Coherent States ◽  
Annihilation Operator ◽  
Single Mode ◽  
Commutation Relations

Three generalized commutation relations for a single mode of the harmonic oscillator which contains para-bose and q oscillator commutation relations are constructed. These are shown to be inequivalent. The coherent states of the annihilation operator for these three cases are also constructed.

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.

Sign in / Sign up

Export Citation Format

Share Document