Damping, field–field correlation and dipole–dipole interaction effects on the entanglement and atomic inversion dynamics

2017 ◽  
Vol 31 (03) ◽  
pp. 1750006
Author(s):  
N. Rustaee ◽  
M. K. Tavassoly ◽  
R. Daneshmand
Keyword(s):  
Population Inversion ◽  
Dynamical Behavior ◽  
Dipole Interaction ◽  
Time Behavior ◽  
Atomic Inversion ◽  
Atomic Dipole ◽  
Quantized Field ◽  
Damped Systems ◽  
Field Correlation ◽  
Degree Of Entanglement

In this paper we study the interaction between two two-level atoms with a two-mode quantized field in the presence of damping. Dipole–dipole interaction between the two atoms and the correlation between the two modes of field are also taken into account. To solve the model, using appropriate transformations, we reduce the considered model to a well-known Jaynes–Cummings model. After finding the analytical solution for the atom–field system, the effects of damping, field–field correlation and atomic dipole–dipole interaction on the entanglement between atoms and population inversion are investigated, numerically. It is observed that the dynamical behavior of the degree of entanglement for damped systems, in relatively large domains of time, takes a low but constant value adequately far from the beginning of the interaction. In addition, it is found that the value of population inversion after the initial oscillations takes negative values for damped systems and eventually vanishes by increasing time. Also, it is seen that simultaneous presence of both dipole–dipole interaction and field–field correlation provides typical collapse–revival phenomenon in the time-behavior of atomic inversion.

The influence of atomic dipole–dipole interaction on the dynamics of the population inversion and entanglement of two atoms interacting non-resonantly with two coupled modes field

2017 ◽  
Vol 31 (05) ◽  
pp. 1750038 ◽  
Author(s):  
Elham Faraji ◽  
Hamid Reza Baghshahi ◽  
Mohammad Kazem Tavassoly
Keyword(s):  
Population Inversion ◽  
Initial Conditions ◽  
Resonance Condition ◽  
Dipole Interaction ◽  
Resonant Interaction ◽  
Von Neumann Entropy ◽  
Coupled Modes ◽  
Von Neumann ◽  
Atomic Dipole ◽  
Down Conversion

In this paper, the non-resonant interaction of two two-level atoms with two quantized cavity fields is studied by considering the dipole–dipole interaction between the two atoms. The correlation between the fields has been taken into account and the parametric down conversion is considered. Under certain initial conditions which is determined for the atoms and the fields, the analytical solution for the time-dependent Schrödinger equation is obtained. Employing this solution, we are able to discuss about some physical properties such as atomic population inversion and entanglement between various subsystems, i.e. “atoms–fields” and “atom–atom” by using respectively von Neumann entropy and negativity. It is deduced from the numerical results that, the mentioned quantities can be controlled by the atomic dipole–dipole interaction and detuning parameter, appropriately. The results show that the degree of entanglement between the two atoms is increased due to the presence of dipole–dipole coupling of the atoms at the beginning of atom–field interaction. Furthermore, it is found that, in the non-resonance condition, the so-called entanglement sudden death occurs in the presence of dipole–dipole interaction.

TIP INSTABILITY DURING CONFINED DIFFUSION-LIMITED GROWTH

1988 ◽  
Vol 02 (08) ◽  
pp. 945-951 ◽  
Author(s):  
DAVID A. KESSLER ◽  
HERBERT LEVINE
Keyword(s):  
Evolution Equations ◽  
Dynamical Behavior ◽  
Stable Steady State ◽  
Time Behavior ◽  
Two Dimensional ◽  
Long Time Behavior ◽  
Limited Growth ◽  
Channel Geometry ◽  
Diffusion Limited ◽  
Long Time

We study diffusion-limited crystal growth in a two dimensional channel geometry. We demonstrate that although there exists a linearly stable steady-state finger solution of the pattern evolution equations, the true dynamical behavior can be controlled by a tip-widening instability. Possible scenarios for the long-time behavior of the system are presented.

scholarly journals THE DYNAMICS OF TACHYON FIELD WITH AN INVERSE SQUARE POTENTIAL IN LOOP QUANTUM COSMOLOGY

2013 ◽  
Vol 22 (06) ◽  
pp. 1350030 ◽  
Author(s):  
FEI HUANG ◽  
JIAN-YANG ZHU ◽  
KUI XIAO
Keyword(s):  
Quantum Cosmology ◽  
Dynamical Behavior ◽  
Loop Quantum Cosmology ◽  
Phase Plane Analysis ◽  
Late Time ◽  
Stable Node ◽  
Time Behavior ◽  
Tachyon Field ◽  
Plane Analysis ◽  
The Stability

The dynamical behavior of tachyon field with an inverse potential is investigated in loop quantum cosmology. It reveals that the late-time behavior of tachyon field with this potential leads to a power-law expansion. In addition, an additional barotropic perfect fluid with the adiabatic index 0 < γ < 2 is added and the dynamical system is shown to be an autonomous one. The stability of this autonomous system is discussed using phase plane analysis. There exist up to five fixed points with only two of them possibly stable. The two stable node (attractor) solutions are specified and their cosmological indications are discussed. For the tachyon dominated solution, the further discussion is stretched to the possibility of considering tachyon field as a combination of two parts which respectively behave like dark matter and dark energy.

scholarly journals Existence and long-time behavior of solutions to the velocity-vorticity-Voigt model of the 3D Navier-Stokes equations with damping and memory

2021 ◽  
Author(s):  
Nguyen Toan
Keyword(s):  
Stokes Equations ◽  
Dynamical Behavior ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Navier Stokes ◽  
Time Behavior ◽  
Navier Stokes Equations ◽  
Long Time ◽  
Voigt Model ◽  
Initial Boundary Value

In this paper, we study the long-time dynamical behavior of the non-autonomous velocity-vorticity-Voigt model of the 3D Navier-Stokes equations with damping and memory. We first investigate the existence and uniqueness of weak solutions to the initial boundary value problem for above-mentioned model. Next, we prove the existence of uniform attractor of this problem, where the time-dependent forcing term $f \in L^2_b(\mathbb{R}; H^{-1}(\Omega))$ is only translation bounded instead of translation compact. The results in this paper will extend and improve some results in Yue, Wang (Comput. Math. Appl., 2020) in the case of non-autonomous and contain memory kernels which have not been studied before.

Atomic motion and dipole–dipole effects on the stability of atom–atom entanglement in Markovian/non-Markovian reservoir

2019 ◽  
Vol 34 (10) ◽  
pp. 1950077 ◽  
Author(s):  
S. Golkar ◽  
M. K. Tavassoly
Keyword(s):  
Weak Coupling ◽  
Initial Conditions ◽  
Dynamical Behavior ◽  
Dipole Interaction ◽  
Zero Temperature ◽  
Entanglement Dynamics ◽  
Entanglement Protection ◽  
Initial States ◽  
The Stability ◽  
Suitable Measure

In this paper, we consider the entanglement dynamics of two identical qubits (two-level atoms) accompanied by dipole–dipole interaction within a common reservoir in the strong and weak coupling regimes. We suppose that the qubits move in the reservoir which is at zero temperature. Using the time-dependent Schrödinger equation, the state vector of the qubits-reservoir system is obtained by which we can evaluate the concurrence as a suitable measure of entanglement between the two qubits. The results show that by choosing special initial conditions for the qubits, a different dynamical behavior of entanglement is visible in such a way that entanglement protection occurs. Also, we find that the qubit motion in the absence of dipole–dipole interaction leads to preservation or at least more slowly decay of entanglement. However, in the presence of dipole–dipole interaction with the movement of qubits, different results can be observed which depend on the initial states of the qubits, i.e. entanglement may or may not be protected.

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.

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.

ON THE NATURE OF FLUORESCENT SPECTRUM OF A TWO ATOM DICKE MODEL IN A NARROW BANDWIDTH SQUEEZED BATH

1994 ◽  
Vol 08 (01n02) ◽  
pp. 121-135 ◽  
Author(s):  
AMITABH JOSHI ◽  
R. R. PURI
Keyword(s):  
Master Equation ◽  
Dipole Interaction ◽  
Spectral Features ◽  
Resonance Fluorescence ◽  
Driving Field ◽  
Narrow Bandwidth ◽  
Fluorescent Spectrum ◽  
Atomic Dipole ◽  
Dicke Model ◽  
Finite Bandwidth

We discuss the spectrum of resonance fluorescence from a system of two identical coherently driven two-level atoms interacting with a finite bandwidth squeezed bath, including the atomic dipole-dipole interaction between the atoms. The characteristics of the spectral features are studied by solving the master equation analytically in the limit of strong driving field. The comparison of these features with respect to an ordinary bath as well as broadband squeezed bath are also presented.

scholarly journals Time-dependent interaction between a two-level atom and a su(1,1) Lie algebra quantum system

2017 ◽  
Vol 31 (15) ◽  
pp. 1750211 ◽  
Author(s):  
M. Sebaweh Abdalla ◽  
E. M. Khalil ◽  
A.-S. F. Obada
Keyword(s):  
Coupling Parameter ◽  
Functional Dependence ◽  
Integrability Condition ◽  
Initial State ◽  
Atomic Inversion ◽  
Mode Field ◽  
Level Atom ◽  
Degree Of Entanglement ◽  
Algebraic Operators ◽  
Dependent Interaction

The problem of the interaction between a two-level atom and a two-mode field in the parametric amplifier-type is considered. A similar problem appears in an ion trapped in a two-dimensional trap. The problem is transformed into an interaction governed by su(1,1) Lie algebraic operators with phase and coupling parameter depending on time. Under an integrability condition, that relates phase and coupling, a solution to the wavefunction is obtained using the Schrödinger equation. The effects of the functional dependence of the coupling and the initial state of the two-level atom on atomic inversion, the degree of entanglement, the fidelity and the Glauber second-order correlation function are investigated. It is shown that the acceleration term plays an important role in controlling the function behavior of the considered quantities.

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