Fluctuations and a rigorous uncertainty relation of trigonometric operators of the phase and the number of photons of an electromagnetic field for general quantum superpositions of coherent states

2017 ◽  
Vol 123 (4) ◽  
pp. 629-641 ◽  
Author(s):  
A. V. Kozlovskii
Keyword(s):  
Electromagnetic Field ◽  
Coherent States ◽  
Uncertainty Relation ◽  
General Quantum ◽  
Quantum Superpositions

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.

scholarly journals REPRESENTATIONS OF GENERALIZED Ar STATISTICS AND EIGENSTATES OF JACOBSON GENERATORS

2006 ◽  
Vol 21 (21) ◽  
pp. 1691-1700 ◽  
Author(s):  
M. DAOUD
Keyword(s):  
Analytic Function ◽  
Coherent States ◽  
Uncertainty Relation ◽  
Fock Space ◽  
Complete Set ◽  
Natural Way

We investigate a generalization of Ar statistics discussed recently in the literature. The explicit complete set of state vectors for the Ar statistics system is given. We consider a Bargmann or an analytic function description of the Fock space corresponding to Ar statistics of bosonic kind. This brings, in a natural way, the so-called Gazeau–Klauder coherent states defined as eigenstates of the Jacobson annihilation operators. The minimization of Robertson uncertainty relation is also considered.

scholarly journals GENERALIZED INTELLIGENT STATES FOR NONLINEAR OSCILLATORS

2001 ◽  
Vol 15 (18) ◽  
pp. 2465-2483 ◽  
Author(s):  
A. H. EL KINANI ◽  
M. DAOUD
Keyword(s):  
Coherent States ◽  
Uncertainty Relation ◽  
Anharmonic Oscillator ◽  
Nonlinear Oscillators ◽  
Analytical Representation

The construction of Generalized Intelligent States (GIS) for the x4-anharmonic oscillator is presented. These GIS families are required to minimize the Robertson–Schrödinger uncertainty relation. As a particular case, we will get the so-called Gazeau–Klauder coherent states. The properties of the latters are discussed in detail. Analytical representation is also considered and its advantage is shown in obtaining the GIS in an analytical way. Further extensions are finally proposed.

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.

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