ENTANGLEMENT OF A TWO-LEVEL ATOM INTERACTING WITH A NEW STRUCTURE OF A GENERALIZED NONLINEAR STARK SHIFT VIA Ξ CONFIGURATION

2011 ◽  
Vol 25 (19) ◽  
pp. 2621-2636 ◽  
Author(s):  
E. M. KHALIL ◽  
M. M. A. AHMED ◽  
A.-S. F. OBADA
Keyword(s):  
Optical Cavity ◽  
Center Of Mass ◽  
Single Mode ◽  
Stark Shift ◽  
Mass Motion ◽  
Shift Parameter ◽  
Atomic Inversion ◽  
Level Atom ◽  
Quantized Field ◽  
Q Function

The problem of a two-level atom interacting with single mode cavity field is considered, however, the optical cavity is filled with new structure of a generalized nonlinear Stark shift via Ξ configuration. One starts with a three-level trapped atom interacting with the quantized field of center of mass motion thus a Hamiltonian for one-phonon process with nonlinearities is derived. Through the elimination of the intermediate level by using the adiabatic elimination method, we generate a new structure of effective Hamiltonian for a two-level atom with a nonlinear Stark shift. The temporal evolution of the atomic inversion is studied, we introduce that in the presence of the Stark shift parameter the atom leaves in a maximal entangled sate. We use the von Neuman entropy to measure the degree of entanglement between the atom and the field. After adding the nonlinear Stark shift the system never reaches the pure state. Also we study the Q-function for obtaining more information in phase space for this system. These aspects are sensitive to changes in the Stark shift parameter. The results shows that the effect of the nonlinearity in the Stark shift changes the quasiperiod of the field entropy and hence the entanglement between the particle and the field.

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.

Quantum phase transition and Berry phase of the Dicke model in the presence of the Stark-shift

2017 ◽  
Vol 31 (12) ◽  
pp. 1750091 ◽  
Author(s):  
A. S. Abdel-Rady ◽  
Samia. S. A. Hassan ◽  
Abdel-Nasser A. Osman ◽  
Ahmed Salah
Keyword(s):  
Phase Transition ◽  
Energy Surface ◽  
Berry Phase ◽  
Optical Cavity ◽  
Mean Field ◽  
Single Mode ◽  
Stark Shift ◽  
Einstein Condensate ◽  
Level Atom ◽  
Dicke Model

In this paper, we employ the energy surface method to study a system of a two-level atom Bose–Einstein condensate coupled to a high-finesse optical cavity interacting with a single-mode electromagnetic field in the presence of the Stark-shift. The energy surface, the Phase transitions and the Berry phase of the two-level atom in Dicke model are obtained. Employing the Holstein–Primakoff representation of the angular momentum Lie algebra, the coupling line separation of the normal phase and the superradiant phase which occurs in a collection of fluorescent emitters (such as atoms), between a state containing few electromagnetic excitations are studied and a mean field description of the Dicke model is presented. We notice that in the thermodynamic limit, the energy surface takes a simple form for a direct description of the phase transition. Moreover, we show that the Stark-shift parameters and the atom–atom interactions can strongly affect the phase transition point. The results in the absence of the Stark-shift agree precisely with those obtained by Li, Liu and Zhou, who studied the same model using a different method.

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.

INTERACTION OF A THREE-LEVEL ATOM WITH A SINGLE-MODE FIELD IN A TWO PHOTON RESONANT CAVITY

2011 ◽  
Vol 25 (03) ◽  
pp. 417-431
Author(s):  
DEBRAJ NATH ◽  
P. K. DAS
Keyword(s):  
Electromagnetic Field ◽  
Resonant Cavity ◽  
Single Mode ◽  
Atomic Level ◽  
Atomic Inversion ◽  
Cooperative Effects ◽  
Two Photon ◽  
Mode Field ◽  
Level Atom ◽  
Successive Passage

In this paper we discuss an extension of Jaynes–Cummings model by adding a further atomic level to support a second resonance and cooperative effects in multi-atom systems. A successive passage of a three-level atom in the V configuration interacting with one quantized mode of electromagnetic field in a cavity will be considered to study atomic inversion and entropy evolution of the state.

REDUCING FOUR-LEVEL TWO-MODE HAMILTONIAN TO AN EFFECTIVE TWO-LEVEL HAMILTONIAN WITH THE ADDITION OF KERR-LIKE MEDIUM

2010 ◽  
Vol 24 (01) ◽  
pp. 109-124 ◽  
Author(s):  
M. A. A. EL-DEBERKY ◽  
M. F. M. ALI
Keyword(s):  
Coherent State ◽  
Cascade Process ◽  
Effective Hamiltonian ◽  
Atomic Inversion ◽  
Level Atom ◽  
Quantized Field

We consider a two-mode quantized field described in a coherent state interacting with a four-level atom. An effective Hamiltonian is obtained by adiabatically eliminating the intermediate two levels in a cascade process. The influence of the Stark shifts and the Kerr-like medium on the atomic inversion are examined, as well as on the field entropy, atomic purity and Mandel's Q-parameter. The results of the calculations are illustrated numerically.

SQUEEZING OSCILLATIONS OF A QUANTIZED FIELD INTERACTING WITH PAIR OF COLD ATOMS VIA INTENSITY-DEPENDENT COUPLING

2007 ◽  
Vol 05 (01n02) ◽  
pp. 199-205 ◽  
Author(s):  
V. I. KOROLI
Keyword(s):  
Cold Atoms ◽  
Exact Analytical Solution ◽  
Single Mode ◽  
Initial Moment ◽  
Transition Elements ◽  
Level Atom ◽  
Field State ◽  
Quantized Field ◽  
Physical Quantities ◽  
Intensity Dependent Coupling

We study the interaction between a single-mode electromagnetic field and a pair of indistinguishable two-level atoms via the intensity-dependent coupling. This problem is equivalent to the equidistant three-level atom with equal dipole moment matrix transition elements between the adjacent levels. The exact analytical solution for the atom–field state-vector is obtained assuming that at the initial moment the field is in the Holstein–Primakoff SU (1,1) coherent state. The quantum statistical and squeezing properties of the field are investigated. The results obtained are compared with those for the single two-level atom obtained by Buzek. We observe that the exact periodicity of the field squeezing that takes place in the case of the single two-level atom is violated in the case of the pair of cold atoms. That is, the exact periodicity of the physical quantities can be destroyed only if the radiation field interacts with a system of more than one two-level atom.

GENERATION OF A NONLINEAR TWO-MODE STARK SHIFT VIA NONDEGENERATE RAMAN TRANSITION

2007 ◽  
Vol 21 (30) ◽  
pp. 5143-5158 ◽  
Author(s):  
E. M. KHALIL
Keyword(s):  
Temporal Evolution ◽  
Stark Shift ◽  
Raman Transition ◽  
Atomic Inversion ◽  
Entropy Squeezing ◽  
Variance Squeezing ◽  
Level Atom ◽  
Quantized Electromagnetic Field ◽  
Schrödinger Picture ◽  
Careful Investigation

In this contribution, a three level atom in interaction with a two-mode quantized electromagnetic field, initially prepared in an entangled two-mode coherent state, is considered. Through the elimination of an intermediate level using the adiabatic elimination method, a nonlinear Stark shift is introduced. The exact solution of the wave function in the Schrödinger picture is obtained. Some statistical aspects through the effective two-level atom interacting with the two-mode and multiphotons processess with the nonlinear Stark shift are presented. The results are employed to perform a careful investigation of the temporal evolution of the atomic inversion, entropy squeezing and variance squeezing. It has been shown that the system is sensitive to any change in the parameter representation of the Stark shift. General conclusions reached are illustrated by numerical results.

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