Steady-state correlations of two atoms interacting with a reservoir

2012 ◽  
Vol 12 (3&4) ◽  
pp. 231-252
Author(s):  
Luis Octavio Castanos
Keyword(s):  
Electromagnetic Field ◽  
Steady State ◽  
Master Equation ◽  
Field Intensity ◽  
Mixed State ◽  
Laser Field ◽  
Quantum Discord ◽  
Energy Levels ◽  
High Laser ◽  
X State

We consider two two-level atoms fixed at different positions, driven by a resonant monochromatic laser field, and interacting collectively with the quantum electromagnetic field. A Born-Markov-secular master equation is used to describe the dynamics of the two atoms and the steady-state is obtained analytically for a configuration of the atoms. The steady-state populations of the energy levels of the free atoms, entanglement, quantum and geometric discords and degree of mixedness are calculated analytically as a function of the laser field intensity and the distance between the two atoms. It is found that there is a possibility of considerable steady-state entanglement and left/right quantum discord and that these can be controlled either by increasing/decreasing the intensity of the laser field or by increasing/decreasing the distance between atoms. It is shown that the system of two atoms can be prepared in a separable mixed state with non-zero quantum discord that turns into an $X$-state for high laser field intensities. The behavior and relationships between the different correlations are studied and several limiting cases are investigated.

scholarly journals HIGH FREQUENCY BEHAVIOR OF THE MAXWELL–BLOCH MODEL WITH RELAXATION: CONVERGENCE TO THE SCHRÖDINGER-RATE SYSTEM

2012 ◽  
Vol 09 (03) ◽  
pp. 355-401
Author(s):  
F. CASTELLA ◽  
E. DUMAS
Keyword(s):  
Electromagnetic Field ◽  
High Frequency ◽  
Laser Field ◽  
Energy Levels ◽  
Photon Emission ◽  
Classical Equation ◽  
Atomic Energy ◽  
Mathematical Framework ◽  
Rate System ◽  
Atomic Energy Levels

We study the Maxwell–Bloch model, which describes the propagation of a laser through a material and the associated interaction between laser and matter (polarization of the atoms through light propagation, photon emission and absorption, etc.). The laser field is described through Maxwell's equations, a classical equation, while matter is represented at a quantum level and satisfies a quantum Liouville equation known as the Bloch model. Coupling between laser and matter is described through a quadratic source term in both equations. The model also takes into account partial relaxation effects, namely the trend of matter to return to its natural thermodynamic equilibrium. The whole system involves 6 + N(N + 1)/2 unknowns, the six-dimensional electromagnetic field plus the N(N + 1)/2 unknowns describing the state of matter, where N is the number of atomic energy levels of the considered material. We consider at once a high frequency and weak coupling situation, in the general case of anisotropic electromagnetic fields that are subject to diffraction. Degenerate energy levels are allowed. The whole system is stiff and involves strong nonlinearities. We show the convergence to a nonstiff, nonlinear, coupled Schrödinger-rate model, involving 3 + N unknowns. The electromagnetic field is eventually described through its envelope, one unknown vector in ℂ3. It satisfies a Schrödinger equation that takes into account propagation and diffraction of light inside the material. Matter on the other hand is described through a N-dimensional vector describing the occupation numbers of each atomic level. It satisfies Einstein's rate equation that describes the jumps of the electrons between the various atomic energy levels, as induced by the interaction with light. The rate of exchange between the atomic levels is proportional to the intensity of the laser field. The whole system is the physically natural nonlinear model. In order to provide an important and explicit example, we completely analyze the specific (two-dimensional) Transverse Magnetic case, for which formulae turn out to be simpler. Technically speaking, our analysis does not enter the usual mathematical framework of geometric optics: it is more singular, and requires an ad hoc Ansatz.

EFFECT OF PHASE FLUCTUATIONS OF LASER ON OPTICAL FORCES IN A TWO-LEVEL ATOM

2000 ◽  
Vol 14 (17n18) ◽  
pp. 631-637 ◽  
Author(s):  
S. V. LAWANDE ◽  
P. V. PANAT
Keyword(s):  
Angular Momentum ◽  
Steady State ◽  
Master Equation ◽  
Gaussian Beam ◽  
Laser Field ◽  
Density Operator ◽  
Bessel Beam ◽  
Optical Forces ◽  
Phase Fluctuations ◽  
Level Atom

An effect of phase fluctuations of a driving laser field on dissipative and dipolar forces of two-level atom is considered. The phase fluctuations are treated by a phase diffusion model where phase fluctuations follow Wiener–Levy process. An exact master equation for the relevant density operator is obtained and solved in the steady state. Optical forces are calculated. The effect of phase fluctuations on angular momentum imparted by a Laguerre–Gaussian beam and an ideal Bessel beam to the atom is investigated.

High-speed isotachophoresis. Analytical aspects of the steady-state longitudinal temperature profiles

1979 ◽  
Vol 44 (3) ◽  
pp. 841-853 ◽  
Author(s):  
Zbyněk Ryšlavý ◽  
Petr Boček ◽  
Miroslav Deml ◽  
Jaroslav Janák
Keyword(s):  
Steady State ◽  
Temperature Distribution ◽  
Electric Field ◽  
Field Intensity ◽  
Electric Field Intensity ◽  
Minor Component ◽  
Physical Models ◽  
Temperature Profiles ◽  
Longitudinal Temperature ◽  
Continuous Character

The problem of the longitudinal temperature distribution was solved and the bearing of the temperature profiles on the qualitative characteristics of the zones and on the interpretation of the record of the separation obtained from a universal detector was considered. Two approximative physical models were applied to the solution: in the first model, the temperature dependences of the mobilities are taken into account, the continuous character of the electric field intensity at the boundary being neglected; in the other model, the continuous character of the electric field intensity is allowed for. From a comparison of the two models it follows that in practice, the variations of the mobilities with the temperature are the principal factor affecting the shape of the temperature profiles, the assumption of a discontinuous jump of the electric field intensity at the boundary being a good approximation to the reality. It was deduced theoretically and verified experimentally that the longitudinal profiles can appreciably affect the longitudinal variation of the effective mobilities in the zone, with an infavourable influence upon the qualitative interpretation of the record. Pronounced effects can appear during the analyses of the minor components, where in the corresponding short zone a temperature distribution occurs due to the influence of the temperatures of the neighbouring zones such that the temperature in the zone of interest in fact does not attain a constant value in axial direction. The minor component does not possess the steady-state mobility throughout the zone, which makes the identification of the zone rather difficult.

Analysis of Vibration Caused by Electromagnetic Force on Stator End-Winding of Large Dry Submersible Motor

2013 ◽  
Vol 416-417 ◽  
pp. 428-432
Author(s):  
Li Shan ◽  
Xiao Wei Cheng ◽  
Yong Fang ◽  
Xiao Hua Bao
Keyword(s):  
Electromagnetic Field ◽  
Steady State ◽  
Transition State ◽  
Electromagnetic Force ◽  
Radial Displacement ◽  
Radial Direction ◽  
Axial Direction ◽  
Axial Displacement ◽  
Force Density ◽  
Submersible Motor

This paper investigates the vibration which caused by electromagnetic on the stator end-winding of the large dry submersible motor. Firstly, the electromagnetic field which included transition state and steady state is researched by 3-D FEM. Secondly, the electromagnetic force which lead to vibrations of end-winding is calculated by numerical method, it can be obtained that where endured the largest force density along the slant part of end-winding. Finally, the radial displacement and the axial displacement of the slant part which caused by vibrations is studied, the analysis results show that the axial displacement is larger than the amplitude of radial displacement. It indicates that the slant part of end-winding will be more easily damaged at axial direction than radial direction.

Force de répulsion entre un courant sinusoïdal linéique et une bande conductrice mince : application aux problèmes de lévitation

1994 ◽  
Vol 72 (9-10) ◽  
pp. 633-638
Author(s):  
M. T. Attaf ◽  
D. Allab
Keyword(s):  
Electromagnetic Field ◽  
Steady State ◽  
Electromagnetic Interaction ◽  
Practical Interest ◽  
Stationary Case ◽  
Electromagnetic Field Distribution ◽  
Conducting Plate ◽  
Conducting Materials ◽  
Sinusoidal Current ◽  
Repulsive Forces

In a previous work, the authors presented a semianalytical treatment of the electromagnetic field distribution in the case of a straight conductor carrying a sinusoidal current parallel to a thin conducting plate. The result of this investigation is extended here to the evaluation of the repulsive forces accompanying this type of electromagnetic interaction. The variation of such forces with geometric parameters is studied in the presence of a single conductor, and in the case of several conductors laying in a plane parallel to the surface of the material submitted to the induction phenomenon. The problem of lévitation in steady-state conditions is examined, in the light of this arrangement, for various conducting materials. Graphs illustrate the results obtained and make evident their practical interest particularly in the stationary case of magnetically levitated vehicles.

Quantum discord and entanglement of two atoms in a micromaser-type system

2016 ◽  
Vol 30 (15) ◽  
pp. 1650190
Author(s):  
Xue-Qun Yan ◽  
Fu-Zhong Wang
Keyword(s):  
Time Evolution ◽  
Mixed State ◽  
Quantum Discord ◽  
Type System ◽  
Complete Loss ◽  
Entangled State ◽  
Fock State

The correlations dynamics of two atoms in the case of a micromaser-type system is investigated. We show that the entangled state can be created by initially maximally mixed state and there exist collapse and revival phenomena for the time evolutions of both entanglement and quantum discord under the system considered as the field is initially in the Fock state. Our results confirm that entanglement and quantum discord have similar behaviors in certain time ranges, such as their oscillations during the time evolution being almost in phase, but they also present significant differences, such as quantum discord being maintained even after the complete loss of entanglement. Furthermore, we exhibit clearly that the dynamics of quantum discord under the action of environment are intimately related to the generation and evolution of entanglement.

Unified approach to solving a steady-state electromagnetic field

1997 ◽  
Vol 33 (2) ◽  
pp. 1974-1977 ◽  
Author(s):  
M. Triep ◽  
B. Hribernik ◽  
L. Skrget
Keyword(s):  
Electromagnetic Field ◽  
Steady State ◽  
Unified Approach

scholarly journals Master equation based steady-state cluster perturbation theory

2015 ◽  
Vol 92 (12) ◽  
Author(s):  
Martin Nuss ◽  
Gerhard Dorn ◽  
Antonius Dorda ◽  
Wolfgang von der Linden ◽  
Enrico Arrigoni
Keyword(s):  
Perturbation Theory ◽  
Steady State ◽  
Master Equation ◽  
Cluster Perturbation Theory

Effects of the Low Frequency Electromagnetic Field on the Centerline Macrosegregation of 7075 Aluminum Ingots

2011 ◽  
Vol 295-297 ◽  
pp. 1705-1708
Author(s):  
Dan Dan Chen ◽  
Hai Tao Zhang ◽  
Xiang Jie Wang ◽  
Jian Zhong Cui
Keyword(s):  
Electromagnetic Field ◽  
Steady State ◽  
Mushy Zone ◽  
Transition Region ◽  
Low Frequency ◽  
Casting Process ◽  
Direct Chill ◽  
Mushy Region ◽  
Chill Casting ◽  
Temperature Contour

The effects of the low frequency electromagnetic field on the macrosegregation of the 7075 aluminum ingots were investigated. The 7075 aluminum ingots with the diameter of 200 mm were prepared by the conventional direct chill casting and the low frequency electromagnetic field casting (LFEC) processes, respectively. The temperature during casting at steady state was measured, and the mushy region was observed from the temperature contour. The concentrations of the alloying elements were measured by the spectrograph. It was found that the transition region was broadened, but the mushy zone became narrower with presence of the low frequency electromagnetic field. The centerline macrosegregation of the ingots was alleviated by the low frequency electromagnetic casting process.

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