Four-level double V-type atomic system solved by virtue of supersymmetric unitary transformation

2021 ◽  
pp. 2150188
Author(s):  
N. H. Abd El-Wahab ◽  
R. A. Zait
Keyword(s):  
Probability Distribution ◽  
Unitary Transformation ◽  
Atomic System ◽  
Single Mode ◽  
Kerr Medium ◽  
Field Mode ◽  
Input Field ◽  
Mode Field ◽  
Q Function ◽  
Supersymmetric Structure

We consider a four-level double V-type atom with two closely-separated top levels and two closely-separated lower levels interacting with a single mode field via multi-photon processes and in the presence of Kerr medium. We show that this atomic system possesses supersymmetric structure and construct its supersymmetric generators. We diagonalize the Hamiltonian of this system using supersymmetric unitary transformation and obtain the corresponding eigenstates and eigenvalues. The atom–field wave functions are obtained when the atom and the field mode are initially in two different cases. The evolution of both the quasi-probability distribution Q-function and the Mandel Q-parameter of the field are studied when the input field is in a coherent state. The influence of the Kerr medium and the detuning parameters on the behavior of these quantum effects is analyzed. The results show that they play a prominent role on the Poissonian statistics of the field. Also, the Kerr medium changes the behavior of the quasi-probability distribution Q-function. We end with discussion and conclusions.

Intensity-dependent and multi-photon Hamiltonian of two two-level atoms and two-mode field in a Kerr medium solved by virtue of supersymmetric unitary transformation

2021 ◽  
pp. 2150060
Author(s):  
N. H. Abd El-Wahab ◽  
R. A. Zait
Keyword(s):  
Unitary Transformation ◽  
Atomic System ◽  
Quantum Effects ◽  
Transformation Method ◽  
Kerr Medium ◽  
Atomic Systems ◽  
Mode Field ◽  
Q Function ◽  
Supersymmetric Structure ◽  
Intensity Dependent Coupling

We consider a generalized multi-photon interaction of two collectively two-level atoms with two-mode of electromagnetic field in the presence of Kerr medium and intensity-dependent coupling. We show that this atomic system possesses supersymmetric structure. We solved this system by virtue of supersymmetric unitary transformation. The supersymmetric generators of this atomic system are constructed. The diagonalization of the corresponding Hamiltonian is performed by introducing a supersymmetric unitary transformation. Accordingly, the eigenvalues and eigenfunctions of the Hamiltonian of the atomic system are obtained. The time evolution of the atom–field wave functions is derived in an exact form for two cases of the initial states of the atoms and the field modes. Some quantum effects such as the second-order correlation function, cross-correlation, purity and Husimi Q-function are investigated. The effects of the Kerr medium, detuning parameter, intensity-dependent coupling and multi-photon transition on the evolution of these quantum effects are examined. We conclude that the supersymmetric unitary transformation method is very simple and can be applied to a variety of atomic systems which possess a supersymmetric structure.

INTENSITY DEPENDENT COUPLING HAMILTONIAN VIA MULTI-PHOTON INTERACTION IN A KERR MEDIUM

2003 ◽  
Vol 17 (30) ◽  
pp. 5795-5810 ◽  
Author(s):  
R. A. ZAIT
Keyword(s):  
Single Mode ◽  
Kerr Medium ◽  
Cavity Field ◽  
Field Mode ◽  
Atomic Inversion ◽  
Two Photon ◽  
Level Atom ◽  
The One ◽  
Q Function ◽  
Quasiprobability Distribution

We study the dynamics and quantum characteristics of a single two-level atom interacting with a single mode cavity field undergoing a multi-photon processes in the presence of a nonlinear Kerr-like medium. The wavefunctions of the multi-photon system are obtained when the atom starts in the excited and in the ground state. The atomic inversion, the squeezing of the radiation field and the quasiprobability distribution Q-function of the field are discussed. Numerical results for these characteristics are presented when the atom starts in the excited state and the field mode in a coherent state. The influence of the presence and absence of the number operator and the Kerr medium for the one- and two-photon processes on the evolution of these characteristics are analyzed.

A FOUR-LEVEL ATOM INTERACTING WITH A SINGLE-MODE CAVITY FIELD: DOUBLE Ξ-CONFIGURATION

2008 ◽  
Vol 22 (26) ◽  
pp. 2587-2599 ◽  
Author(s):  
N. H. ABDEL-WAHAB
Keyword(s):  
Coherent State ◽  
Time Evolution ◽  
Single Mode ◽  
Cavity Field ◽  
Field System ◽  
Input Field ◽  
Level Atom ◽  
Constants Of Motion ◽  
Q Function ◽  
Single Mode Cavity

In this article, the problem of a double Ξ-type four-level atom interacting with a single-mode cavity field is considered. The considered model describes several distinct configurations of a four-level atom. Also, this model includes the detuning parameters of the atom-field system. We obtain the constants of motion and the wavefunction is derived when the atom is initially prepared in the upper state. We used this model for computing a number of the field aspects for the considered system. As an illustration, the model is used for studying the time evolution of the Mandel Q-parameter, amplitude-squared squeezing phenomenon and Q-function when the input field is considered in a coherent state. The results show that these phenomena are affected by the presence of detuning parameters.

scholarly journals Quantumness Measures for a System of Two Qubits Interacting with a Field in the Presence of the Time-Dependent Interaction and Kerr Medium

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 635
Author(s):  
Sayed Abdel-Khalek ◽  
Kamal Berrada ◽  
Eied M. Khalil ◽  
Abdel-Shafy F. Obada ◽  
Esraa Reda ◽  
...  
Keyword(s):  
Single Mode ◽  
Dynamical Behaviour ◽  
Time Dependent ◽  
Von Neumann Entropy ◽  
Kerr Medium ◽  
Von Neumann ◽  
Mode Field ◽  
Mandel’S Parameter ◽  
Qubit System ◽  
Dependent Interaction

In this work, we introduce the standard Tavis-Cummings model to describe two-qubit system interacting with a single-mode field associated to power-law (PL) potentials. We explore the effect of the time-dependent interaction and the Kerr-like medium. We solve the Schrödinger equation to obtain the density operator that allows us to investigate the dynamical behaviour of some quantumness measures, such as von Neumann entropy, negativity and Mandel’s parameter. We provide how these entanglement measures depend on the system parameters, which paves the way towards better control of entanglement generation in two-qubit systems. We find that the enhancement and preservation of the atoms-field entanglement and atom-atom entanglement can be achieved by a proper choice of the initial parameters of the field in the absence and presence of the time-dependent interaction and Kerr medium. We examine the photons distribution of the field and determine the situations for which the field exhibits super-poissonian, poissonian or sub-poissonian distribution.

A STUDY OF THE INTERACTION BETWEEN A FIVE-LEVEL ATOM AND A SINGLE-MODE CAVITY FIELD: FAN-TYPE

2011 ◽  
Vol 25 (24) ◽  
pp. 1971-1982 ◽  
Author(s):  
N. H. ABDEL-WAHAB
Keyword(s):  
Dynamical Behavior ◽  
Single Mode ◽  
Kerr Nonlinearity ◽  
Coupling Constants ◽  
Kerr Medium ◽  
Cavity Field ◽  
Atomic Inversion ◽  
Input Field ◽  
Level Atom ◽  
Single Mode Cavity

In this paper, a model describing the interaction of a five-level (85 Rb ) atom with one-mode cavity field including Kerr nonlinearity is discussed. Analytical solution for this model is presented when the atom is initially prepared in its upper state. The obtained results are then employed to examine the dynamical behavior of atomic inversion, field statistics and field squeezing when the input field is initially considered in a coherent state. It is found that the atom-field properties are influenced by the changing of the coupling constants, the detuning parameters and the Kerr medium.

scholarly journals A deformed model for N-type four-level atom and a single mode field system in the presence of the Kerr medium

2021 ◽  
Author(s):  
N.H. Abdel-Wahab ◽  
S. Abdel-Khalek ◽  
E.M. Khalil ◽  
Nawal Alshehri
Keyword(s):  
Geometric Phase ◽  
Nonlinear Medium ◽  
Single Mode ◽  
Medium Effect ◽  
Kerr Medium ◽  
Resonance Case ◽  
Coupling Interaction ◽  
Field System ◽  
Mode Field ◽  
Level Atom

Abstract The aim of this paper is to study the interaction between a single mode field and four-level atom in N - configuration under nonlinear medium effect. The non-resonance case and the deformation forms in the coupling interaction between the field and the atom are included. The wave function of the proposed system is obtained when the atom is prepared initially in its excited state while the field is prepared in a coherent state. The effect of the deformation and nonlinear medium on the temporal behavior of collapse-revival, field entropy and geometric phase of the system are examined. The results show that the presence of the intensity of the coupling interaction and the non-linear medium have an important influence on the properties of these phenomena.

A MOVING RUBIDIUM ATOM INTERACTING WITH A SINGLE MODE CAVITY FIELD IN THE PRESENCE OF KERR MEDIUM

2004 ◽  
Vol 18 (21n22) ◽  
pp. 1087-1100 ◽  
Author(s):  
R. A. ZAIT ◽  
N. H. ABD EL-WAHAB
Keyword(s):  
Equations Of Motion ◽  
Single Mode ◽  
Kerr Medium ◽  
Cavity Field ◽  
Rubidium Atom ◽  
Exactly Solvable ◽  
Rotating Wave ◽  
Basic Equations ◽  
Q Function ◽  
Single Mode Cavity

We study the interaction between a moving four-level rubidium atom and a single mode cavity field in the presence of a nonlinear Kerr-like medium. We derive the basic equations of motion for the atomic system and show that it is exactly solvable in the rotating wave approximation. The momentum increment, the momentum diffusion and the quasi-probability distribution Q-function of this system are studied. We investigate numerically the influence of the Kerr medium on the evolution of the previous statistical properties in the exact resonant and nonresonant cases where the atom is initially in the ground state and the field is in a coherent state. It is found that the Kerr medium has an important effect on their evolutions. Finally, conclusions and discussion are given.

Mode field diameter measurement conditions in single-mode fibres

1989 ◽  
Vol 25 (8) ◽  
pp. 493
Author(s):  
M. Ohashi ◽  
N. Shibata ◽  
K. Sato
Keyword(s):  
Single Mode ◽  
Diameter Measurement ◽  
Mode Field ◽  
Mode Field Diameter

GEOMETRIC PHASE AND DISENTANGLEMENT OF A MOVING FOUR-LEVEL ATOM IN THE PRESENCE OF NONLINEAR MEDIUM

2012 ◽  
Vol 10 (01) ◽  
pp. 1250007 ◽  
Author(s):  
NOUR ZIDAN ◽  
S. ABDEL-KHALEK ◽  
M. ABDEL-ATY
Keyword(s):  
System Dynamics ◽  
Geometric Phase ◽  
Nonlinear Medium ◽  
Atomic Motion ◽  
Kerr Medium ◽  
Mode Structure ◽  
Field Mode ◽  
Level Atom

In this paper, we investigate the geometric phase of the field interacting with a moving four-level atom in the presence of Kerr medium. The results show that the atomic motion, the field-mode structure and Kerr medium play important roles in the evolution of the system dynamics. As illustration, we examine the behavior of the geometric phase and entanglement with experimentally accessible parameters. Some new aspects are observed and discussed.

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