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At least 1,711 records · Page 95
All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

Global, quasi-steady dynamics of the distant solar wind 2: Deformation of the heliospheric current sheet

A three-dimensional (3-D) magnetohydrodynamic (MHD) numerical model is used to trace global deformations of the heliospheric current sheet (HCS) caused by large-scale dynamical interactions associated with corotating solar wind flows. Configurations incorporating the tilted-dipole geometry are investigated out past 30 AU for a variety of dipole tilt angles, alpha. Inclusion of the full, 3-D interplanetary dynamics allows north-south displacements and the east-west warping of the HCS by advective corotational effects to be accurately assessed for the first time. It is found that large-scale spatial correlations between velocity and density imposed at the coronal source (i.e., the geometric arrangement whereby regions of high-speed low-density material lying adjacent to areas of slow, dense flow interact obliquely under the influence of solar rotation) result in a distinctive pattern of deformation of the HCS. For an alpha = 30 deg tilted-dipole example, it is shown that typical zonal variations in radial velocity lead to significant folding of the HCS within about 5 AU of the Sun. By 10 AU, additional sharp bends appear near the latitudinal extremes of the HCS surface, where it is overtaken by shock fronts driven by 3-D corotating interaction regions (CIRs). Moreover, the model suggests that inside about 20 AU, major plasma structures are systematically organized, about the HCS, such that the greatest concentrations of material and magnetic field (the centroids of the 3-D CIR structures) are coincident with the folded crests of the HCS (near heliographic latitudes lambda = +/- alpha). Thus, in these circumstances many of the more interesting dynamical features inconveniently lie well away from the heliographic equator. At larger heliocentric distances, where neighboring CIRs begin to interact strongly, the warping of the HCS abates dramatically and the association between folds in the HCS and major field and density concentrations is weakened and ultimately breaks down. On the basis of the model calculations, quasi-steady deformations and related phenomena should figure prominently in the interplanetary medium, except during those periods when the magnetic dipole and solar spin axes are nearly aligned (alpha is approximately less than 10 deg). Even then, they may be of significance if there are any substantial local warps or kinks in the streamer belt.

Pizzo, V. J.↗
NASA NTRS1999

Molecular Modeling of the Poling of Piezoelectric Polyimides

The computational method described in this paper allows the calculation of the dielectric relaxation strength of an amorphous polymer based solely upon its chemical structure. The 4,4' oxydiphthalic anhydride (ODPA) dianhydride and bis-aminophenoxybenzene (APB) diamine based polyimides, (beta-CN) APB-ODPA and APB-ODPA were studied. Amorphous cells were constructed and then poled using molecular dynamics. Dielectric relaxation strengths of Delta(epsilon) = 17.8 for (beta-CN) APB-ODPA and Delta(epsilon) = 7.7 for APB-ODPA were predicted. These values are in excellent agreement with the experimental values. It was found that both the pendant nitrile dipole and the backbone anhydride residue dipole make significant contributions to the polyimides dielectric response. Specifically, it was shown that the difference in the magnitude of the dielectric relaxations is directly attributable to the nitrile dipole. The size of the relaxations indicate an absence of cooperative dipolar motions, The model was used to explain these results in terms of the average orientation of the nitrile and anhydride dipoles to within 51 deg. and 63 deg., respectively, of the applied electric field.

Young, J. A.↗
NASA NTRS1999

Microgravity Experiments to Evaluate Electrostatic Forces in Controlling Cohesion and Adhesion of Granular Materials

The bulk behavior of dispersed, fluidized, or undispersed stationary granular systems cannot be fully understood in terms of adhesive/cohesive properties without understanding the role of electrostatic forces acting at the level of the grains themselves. When grains adhere to a surface, or come in contact with one another in a stationary bulk mass, it is difficult to measure the forces acting on the grains, and the forces themselves that induced the cohesion and adhesion are changed. Even if a single grain were to be scrutinized in the laboratory, it might be difficult, perhaps impossible, to define the distribution and character of surface charging and the three-dimensional relationship that charges (electrons, holes) have to one another. The hypothesis that we propose to test in microgravity (for dielectric materials) is that adhesion and cohesion of granular matter are mediated primarily by dipole forces that do not require the presence of a net charge; in fact, nominally electrically neutral materials should express adhesive and cohesive behavior when the neutrality results from a balance of positive and negative charge carriers. Moreover, the use of net charge alone as a measure of the electrical nature of grain-to-grain relationships within a granular mass may be misleading. We believe that the dipole forces arise from the presence of randomly-distributed positive and negative fixed charge carriers on grains that give rise to a resultant dipole moment. These dipole forces have long-range attraction. Random charges are created whenever there is triboelectrical activity of a granular mass, that is, whenever the grains experience contact/separation sequences or friction.

Marshall, J.↗
NASA NTRS2001

The UAH Spinning Terrella Experiment: A Laboratory Analog for the Earth's Magnetosphere

The UAH Spinning Terrella Experiment has been modified to include the effect of a second magnet. This is a simple laboratory demonstration of the well-known double-dipole approximation to the Earth's magnetosphere. In addition, the magnet has been biassed $\sim$-400V which generates a DC glow discharge and traps it in a ring current around the magnet. This ring current is easily imaged with a digital camera and illustrates several significant topological properties of a dipole field. In particular, when the two dipoles are aligned, and therefore repel, they emulate a northward IMF Bz magnetosphere. Such a geometry traps plasma in the high latitude cusps as can be clearly seen in the movies. Likewise, when the two magnets are anti-aligned, they emulate a southward IMF Bz magnetosphere with direct feeding of plasma through the x-line. We present evidence for trapping and heating of the plasma, comparing the dipole-trapped ring current to the cusp-trapped population. We also present a peculiar asymmetric ring current produced in by the plasma at low plasma densities. We discuss the similarities and dissimilarities of the laboratory analog to the collisionless Earth plasma, and implications for the interpretation of IMAGE data.

Sheldon, R. B.↗
NASA NTRS1999

On Europa's Magnetospheric Interaction: A MHD Simulation of the E4 Flyby

The global three-dimensional interaction of Europa with the Jovian magnetosphere is modeled by using a complete set of ideal magnetohydrodynamic (MHD) equations. The model accounts for exospheric mass loading, ion-neutral charge exchange, recombination, and a possible intrinsic dipole magnetic field of Europa. The single-fluid MHD equations are solved by using a modem, finite volume, higher-order, Godunov-type method on an adoptively refined unstructured grid, which allows detailed modeling of the region near Europa while still resolving both the upstream region and the satellite's wake. The magnetic field and plasma density measured during Galileo's EGA flyby of December 19, 1996, are reproduced reasonably well in the simulation. We find the agreement between the data and our model particularly convincing if we assume that the plasma velocity during the EGA flyby deviated from the nominal corotation direction by approximately 20 deg. Evidence from the Galileo energetic particle detector also supports this assumption. In this case, we can fit the data using a dipole with orientation close to that of an induced dipole arising from the interaction of a hypothetical conducting subsurface layer on Europa with the periodically changing magnetic field of Jupiter. However, the magnitude of the dipole in our model is somewhat smaller (70%) than that suggested by Khurana et al. The total mass loading and ion-neutral charge exchange rates are consistent with the estimates of Europa's atmosphere and ionosphere.

Kabin, K.↗
NASA NTRS2004

Electrostatics of Granular Materials

The purpose of the research was to continue developing an understanding of electrostatic phenomena in preparation for any future flight opportunities of the EGM experiment, originally slated for a 2004 Space Station deployment. Work would be based on theoretical assessments, ground-based lab experiments, and reduced-gravity experiments. The ability to examine dipoles in the lab proved to be elusive, and thus, effort was concentrated on monopoles -how materials become charged, the fate of the charge, the role of material type, and so forth. Several significant milestones were achieved in this regard. In regard of the dipoles, experiments were designed in collaboration with the University of Chicago school district who had access to reduced gravity on the KC-135 aircraft. Two experiments were slated to fly last year but were cancelled after the Columbia accident. One of the experiments has been given a second life and will fly sometime in 2005 if the Shuttle flights resume. There remains active interest in the question of electrostatic dipoles within the educational community, and experiments using magnetic dipoles as a substitute are to be examined. The KC-135 experiments will also examine dispersion methods for particles as a verification of possible future techniques in microgravity. Both laboratory and theoretical work established a number of breakthroughs in our understanding of electrostatic phenomena. These breakthroughs are listed in this paper.

Marshall, John↗
NASA NTRS2009

Subcritical-Water Extraction of Organics from Solid Matrices

An apparatus for extracting organic compounds from soils, sands, and other solid matrix materials utilizes water at subcritical temperature and pressure as a solvent. The apparatus, called subcritical water extractor (SCWE), is a prototype of subsystems of future instrumentation systems to be used in searching for organic compounds as signs of past or present life on Mars. An aqueous solution generated by an apparatus like this one can be analyzed by any of a variety of established chromatographic or spectroscopic means to detect the dissolved organic compound( s). The apparatus can be used on Earth: indeed, in proof-of-concept experiments, SCWE was used to extract amino acids from soils of the Atacama Desert (Chile), which was chosen because the dryness and other relevant soil conditions there approximate those on Mars. The design of the apparatus is based partly on the fact that the relative permittivity (also known as the dielectric constant) of liquid water varies with temperature and pressure. At a temperature of 30 C and a pressure of 0.1 MPa, the relative permittivity of water is 79.6, due to the strong dipole-dipole electrostatic interactions between individual molecular dipoles. As the temperature increases, increasing thermal energy causes increasing disorientation of molecular dipoles, with a consequent decrease in relative permittivity. For example, water at a temperature of 325 C and pressure of 20 MPa has a relative permittivity of 17.5, which is similar to the relative permittivities of such nonpolar organic solvents as 1-butanol (17.8). In the operation of this apparatus, the temperature and pressure of water are adjusted so that the water can be used in place of commonly used organic solvents to extract compounds that have dissimilar physical and chemical properties.

Amashukeli, Xenia↗
NASA NTRS2010

A New Measurement of the Bulk Flow of X-Ray Luminous Clusters of Galaxies

We present new measurements of the large-scale bulk flows of galaxy clusters based on five-year WMAP data and a significantly expanded X-ray cluster catalog. Our method probes the flow via measurements of the kinematic Sunyaev-Zel'dovich (SZ) effect produced by the hot gas in moving clusters. It computes the dipole in the cosmic microwave background data at cluster pixels, which preserves the SZ component while integrating down other contributions. Our improved catalog of over 1000 clusters enables us to further investigate possible systematic effects and, thanks to a higher median cluster redshift, allows us to measure the bulk flow to larger scales. We present a corrected error treatment and demonstrate that the more X-ray luminous clusters, while fewer in number, have much larger optical depth, resulting in a higher dipole and thus a more accurate flow measurement. This results in the observed correlation of the dipole derived at the aperture of zero monopole with the monopole measured over the cluster central regions. This correlation is expected if the dipole is produced by the SZ effect and cannot be caused by unidentified systematics (or primary cosmic microwave background anisotropies). We measure that the flow is consistent with approximately constant velocity out to at least [similar, equals]800 Mpc. The significance of the measured signal peaks around 500 h -1 70 Mpc, most likely because the contribution from more distant clusters becomes progressively more diluted by the WMAP beam. However, at present, we cannot rule out that these more distant clusters simply contribute less to the overall motion.

Kashlinsky, A.↗
NASA NTRS2012

Broadband Spectroscopy Using Two Suzaku Observations of the HMXB GX 301-2

We present the analysis of two Suzaku observations of GX 301-2 at two orbital phases after the periastron passage. Variations in the column density of the line-of-sight absorber are observed, consistent with accretion from a clumpy wind. In addition to a CRSF, multiple fluorescence emission lines were detected in both observations. The variations in the pulse profiles and the CRSF throughout the pulse phase have a signature of a magnetic dipole field. Using a simple dipole model we calculated the expected magnetic field values for different pulse phases and were able to extract a set of geometrical angles, loosely constraining the dipole geometry in the neutron star. From the variation of the CRSF width and energy, we found a geometrical solution for the dipole, making the inclination consistent with previously published values.

Suchy, Slawomir↗
NASA NTRS2018

Li(+)-ligand Binding Energies and the Effect of Ligand Fluorination on the Binding Energies

The Li(+)-ligand binding energies are computed for seven ligands and their perfluoro analogs using Density Functional Theory. The bonding is mostly electrostatic in origin. Thus the size of the binding energy tends to correlate with the ligand dipole moment, however, the charge-induced dipole contribution can be sufficiently large to affect the dipole-binding energy correlation. The perfluoro species are significantly less strongly bound than their parents, because the electron withdrawing power of the fluorine reduces the ligand dipole moment.

Charles W Bauschlicher↗
NASA NTRSDate not supplied

Correlated Electromagnetic Levitation Actuator: A Reaction Sphere Based Attitude Control System

To address problems experienced by current reaction wheels and control moment gyroscopebased attitude control systems (ACS), researchers at NASA’s Marshall Space Flight Center have begun developing a reaction sphere actuator based on correlated electromagnetic levitation that will be immune to destructive bearing friction, momentum saturation, and gimbal lock. The Correlated Electromagnetic Levitation Actuator (CELA) advances the state of the art of reaction sphere ACSs by employing the concept of correlated magnetics. It is a frictionless, direct-drive reaction sphere that harnesses a unique technology with an array of applications across multiple disciplines. Correlated electromagnets function in a manner that is analogous to a matched filter; the convolution of two signals is peaked at the index representing the greatest match. For CELA, the signals are the patterns of magnetic flux density as a function of position. The magnitude of the convolution equates to an attractive or repulsive force, and these forces can be azimuthal or radial. The development of CELA is based in four distinct disciplines: Advanced Manufacturing, Prototype Development, Electromagnetic Modeling, and Controls. We are developing novel manufacturing techniques required to build arrays of permanent and electromagnet dipoles on curved surfaces. To print the permanent magnetic array, we have developed a probe with pyramidal magnets that will reside on a robotic arm to induce localized magnetic fields on a surface. The probe also includes the ability to erase dipole patterns from a permanent magnet by heating the surface to its Curie temperature. A number of test articles and prototypes have been developed using additive manufacturing methods. These prototypes have included hemispherical motors to test the drive algorithm, and a levitation test bed that demonstrates a magnetic bearing method based on attractive magnetic forces and ratiometric Hall effect sensors. We developed an array of electromagnetic dipoles on a printed circuit board (PCB) with individual H-bridges controlling each coil. This device created various flux density patterns and we measured their magnetic fields using a custom Hall effect 3-D probe and a LabVIEW virtual instrument. These data will serve as a benchmark for characterizing the accuracy of future models. Current work is focused on modeling the magnetic fields of our prototype arrays using COMSOL Finite Element Analysis and verifying the model against our test data. Accurate modeling will allow us to quickly test new patterns of electromagnets and their macro behavior. Eventually, the magnetic field models will be implemented in our controls simulations to facilitate precise control of the reaction sphere. Initial model results agree with field measurements to within 1 G (5% of measured flux density). Currently, we are testing different material properties of the electromagnets and their magnetic fields and thermal effects. These results will be used to refine the design of the electromagnetic dipoles. Our control efforts have centered on developing commutation, levitation, and field pattern shaping hardware in the form of breadboards and PCBs with software running on a local microcontroller. In addition, our partners developed MATLAB Simulink models to demonstrate a PID controller thatmitigates disturbance forces resulting from the interaction of drive and levitation magnetics. Finally, we have designed a three-axis test stand that will be used in future work to demonstrate CELA’s orientation control capability.

controls↗
NASA NTRSDate not supplied

Correlated Electromagnetic Levitation Actuator: A Reaction Sphere-Based Attitude Control System

To address problems experienced by current reaction wheels and control moment gyroscopebased attitude control systems (ACS), researchers at National Aeronautics and Space Administration’s (NASA’s) Marshall Space Flight Center (MSFC) have begun developing a reaction sphere actuator based on correlated electromagnetic levitation that will be immune to destructive bearing friction, momentum saturation, and gimbal lock. The Correlated Electromagnetic Levitation Actuator (CELA) advances the state of the art of reaction sphere ACSs by employing the concept of correlated magnetics. It is a frictionless, direct-drive reaction sphere that harnesses a unique technology with an array of applications across multiple disciplines. Correlated electromagnets function in a manner that is analogous to a matched filter; the convolution of two signals is peaked at the index representing the greatest match. For CELA, the signals are the patterns of magnetic flux density as a function of position. The magnitude of the convolution equates to an attractive or repulsive force, and these forces can be azimuthal or radial. The development of CELA is based in four distinct disciplines: Advanced Manufacturing, Prototype Development, Electromagnetic Modeling, and Controls. We are developing novel manufacturing techniques required to build arrays of permanent and electromagnet dipoles on curved surfaces. To print the permanent magnetic array, we have developed a probe with pyramidal magnets that will reside on a robotic arm to induce localized magnetic fields on a surface. We have also used high temperature ovens to erase dipole patterns from a permanent magnet by heating the surface to its Curie temperature. A number of test articles and prototypes have been developed using additive manufacturing methods. These prototypes have included hemispherical motors to test the drive algorithm, and a levitation test bed that demonstrates a magnetic bearing method based on attractive magnetic forces and ratiometric Hall effect sensors. We developed an array of electromagnetic dipoles on a printed circuit board (PCB) with individual H-bridges controlling each coil. This device created various flux density patterns and we measured their magnetic fields using a custom Hall effect 3-D probe and a LabVIEW virtual instrument. These data will serve as a benchmark for characterizing the accuracy of future models. Current work is focused on modeling the magnetic fields of our prototype arrays using COMSOL finite element analysis (FEA) and verifying the model against our test data. Accurate modeling will allow us to quickly test new patterns of electromagnets and their macro behavior. Eventually, the magnetic field models will be implemented in our controls simulations to facilitate precise control of the reaction sphere. Initial model results agree with field measurements to within 1 G (5% of measured flux density). Currently, we are testing different material properties of the electromagnets and their magnetic fields and thermal effects. These results will be used to refine the design of the electromagnetic dipoles. Our control efforts have centered on developing commutation, levitation, and field pattern shaping hardware in the form of breadboards and PCBs with software running on a local microcontroller. In addition, our partners developed MATLAB Simulink models to demonstrate a PID controller that mitigates disturbance forces resulting from the interaction of drive and levitation magnetics. Finally, we have designed a three-axis test stand that will be used in future work to demonstrate CELA’s orientation control capability.

reaction sphere↗
NASA NTRS2018

Quantitative validation of Ames IR intensity and new line lists for (32/33/34)S(16)O2, (32)S(18)O2 and (16)O(32)S(18)O

The quality of Ames-296K SO2 Infrared (IR) line list intensities is first validated by quantitative exploration of several dipole moment surfaces (DMSs) and partition sum convergence. The DMSs are computed with several of Dunning’s correlation-consistent basis sets and their vibrational dependence are compared to the empirical model derived from Stark effect experiments reported by D. Patel, D. Margolese, and T.R. Dykea [J.Chem.Phys. 70, 2740 (1979)]. The effective dipole deviations from the DMS adopted in the Ames IR lists is 0.2-0.4% for vibrational states up to 3v3. The vibrational dependence of the dipole moment is also in good agreement, except for nv1. Partition sum convergence at 296K is confirmed by new calculations with rotational quantum number J up to 150 and upper state E’ up to 8000 cm-1. The isotopologue consistency of the Ames IR line lists is superior relative to the regular Effective Hamiltonian (EH) models and Effective Dipole Moment (EDM) models. The v1+v2 and v2+v3 intensity consistency check reveals the recently reported experimental intensities need significant improvement or re-analysis. After the accuracy, convergence, and isotopologue consistency have been confirmed, the theoretical Ames-296K intensities are combined with the experimental line positions or EH models that experimental spectroscopists published after 2009. Three high-resolution IR line sets are reported for the (32/33/34)S(16)O2, (32)S(18)O2 and (16)O(32)S(18)O isotopologues: (1) the “New Lines Sets” include experimentally measured line positions; (2) the “Expanded Line Sets” include possible transitions among new rovibrational levels assigned in experiments and ground state (GS) levels predicted by reliable EH models; (3) the “Ames + MARVEL Sets” include possible transitions among all those levels reported in a recent MARVEL analysis. [Tóbiás et al, JQSRT 208, 152 (2018)]. Compared to the limited data in High-resolution TRANsmission molecular absorption database (HITRAN), these line sets have significantly improved the data coverage up to 4000 cm-1. Some missing bands can be traced to the unpublished experimental data. The isotopologue consistency of these line sets will help identify the uncertainties and defects in the experimental EH and EDM models. These line sets are good candidates for the next HITRAN update, if line shape parameters are available. The line sets can be downloaded from supplementary files or from the Ames Molecular Spectroscopic Database at http://huang.seti.org.

Xinchuan Huang↗
DOE OSTI2013

Molecular Simulation of Water Extraction into a Tri-n-Butyl-Phosphate/n-Dodecane Solution

Abstract: Molecular dynamics simulations were performed to investigate water extraction into a solution of 30 vol% tri-n-butyl-phosphate (TBP) in n-dodecane. This solvent extraction mixture is commonly used in hydrometallurgical and nuclear fuel recycling operations for recovering metals from aqueous streams. It is known that water is coextracted in the organic phase and that it competes with metal ions for the available extractant agent (TBP). Therefore investigating pure water extraction provides a realistic prototype to test molecular simulation methods for the first time in this area. Our computational results indicate that the TBP electric dipole moment has a significant effect on the predicted water solubility. A larger TBP dipole moment decreases the aqueous-organic interfacial tension, leading to increased roughness of the aqueous-organic interface. Interfacial roughness has a significant effect on disrupting the interfacial water hydrogen bonding structure, resulting in a greater number of dangling water molecules at the interface. This enhances the probability of water molecules to break away from the aqueous phase and to migrate into the bulk of the organic phase. Therefore, the magnitude of the TBP dipole moment is a crucial factor in controlling water hydrogen bond breaking at the aqueous-organic interface. By slightly lowering the atomic partial charges of the TBP atoms, to produce a dipole moment that better agrees with experimental data, we were able to predict water solubility in close agreement with experimental measurements. Hence we demonstrate that a molecular modeling and simulation approach may provide quantitative support to experimental programs in this area. In addition, our simulation results shed light into the molecular mechanism of water extraction, the critical role of TBP, and the structural forms of water molecules both at the interface and in the bulk of the organic phase. Specifically, it is found that water molecules are extracted either as single molecules or as clusters. Furthermore, within the organic phase, the extracted water forms clusters with up to 20 water molecules, however, more than 70% of these water clusters contain less than 5 water molecules when the water extraction process reaches saturation.

de Almeida, Valmor F↗
DOE OSTI2013

Enhanced phase segregation induced by dipolar interactions in polymer blends

We present a generalized theory for studying phase separation in polymer blends containing dipoles on their backbone. The theory is used to construct co-existence curves and study the effects of dipolar interactions on interfacial tension for a planar interface between the coexisting phases. It is shown that mismatch in monomeric dipole moments leads to destabilization of homogeneous phase. Corrections to the Flory-Huggins phase diagram are predicted using the theory. Furthermore, it is found that interfacial tension increases with an increase in the mismatch. Density profiles and interfacial tensions are constructed for diffuse and sharp polymer-polymer interfaces by extending Cahn-Hilliard and Helfand-Tagami-Sapse s treatment, respectively. Correlating dipole moments with the dielectric constant of pure phases, it is demonstrated that effects of mismatch between the dipole moments of the two monomers is equivalent to the dielectric mismatch between the polymers.

Kumar, Rajeev↗
DOE OSTI2018

Method and apparatus for quantum information processing using entangled neutral-atom qubits

A method for preparing an entangled quantum state of an atomic ensemble is provided. The method includes loading each atom of the atomic ensemble into a respective optical trap; placing each atom of the atomic ensemble into a same first atomic quantum state by impingement of pump radiation; approaching the atoms of the atomic ensemble to within a dipole-dipole interaction length of each other; Rydberg-dressing the atomic ensemble; during the Rydberg-dressing operation, exciting the atomic ensemble with a Raman pulse tuned to stimulate a ground-state hyperfine transition from the first atomic quantum state to a second atomic quantum state; and separating the atoms of the atomic ensemble by more than a dipole-dipole interaction length.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

Entanglement Created by Dissipation

A technique for entangling closely separated atoms by the process of dissipative spontaneous emission is presented. The system considered is composed of two non-identical two-level atoms separated at the quarter wavelength of a driven standing wave laser field. At this atomic distance, only one of the atoms can be addressed by the laser field. In addition, we arrange the atomic dipole moments to be oriented relative to the inter-atomic axis such that the dipole-dipole interaction between the atoms is zero at this specific distance. It is shown that an entanglement can be created between the atoms on demand by tuning the Rabi frequency of the driving field to the difference between the atomic transition frequencies. The amount of the entanglement created depends on the ratio between the damping rates of the atoms, but is independent of the frequency difference between the atoms. We also find that the transient buildup of an entanglement between the atoms may differ dramatically for different initial atomic conditions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗