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NASA NTRS2012

Modeling the Flow of Rarefied Gases at NASA

At modest temperatures, the thermal energy of atmospheric diatomic gases such as nitrogen is primarily distributed between only translational and rotational energy modes. Furthermore, these energy modes are fully excited such that the specific heat at constant volume is well approximated by the simple expression C(sub v) = 5/2 R. As a result, classical mechanics provides a suitable approximation at such temperatures of the true quantum mechanical behavior of the inter-molecular collisions of such molecules. Using classical mechanics, the transfer of energy between rotational and translation energy modes is studied. The approach of Lordi and Mates is adopted to compute the trajectories and time dependent rotational orientations and energies during the collision of two non-polar diatomic molecules. A Monte-Carlo analysis is performed collecting data from the results of many such simulations in order to estimate the rotational relaxation time. A Graphical Processing Unit (GPU) is employed to improve the performance of the Monte-Carlo analysis. A comparison of the performance of the GPU implementation to an implementation on traditional computer architecture is made. Effects of the assumed inter-molecular potential on the relaxation time are studied. The seminar will also present highlights of computational analyses performed at NASA Johnson Space Center of heat transfer in rarefied gases.

Forrest E. Lumpkin, III↗
NASA NTRS2007

Quantum Chemical Evaluation of the Astrochemical Significance of Reactions between S Atom and Acetylene or Ethylene

Addition-elimination reactions of S atom in its P-3 ground state with acetylene (C2H2) and ethylene (C2H4) were characterized with both molecular orbital and density functional theory calculations employing correlation consistent basis sets in order to assess the likelihood either reaction might play a general role in astrochemistry or a specific role in the formation of S2 (X (sup 3 SIGMA (sub g) (sup -)) via a mechanism proposed by Saxena and Misra (Mon. Not. R. Astron. Soc. 1995, 272, 89). The acetylene and ethylene reactions proceed through C2H2S ((sup 3)A")) and C2H4S ((sup 3)A")) intermediates, respectively, to yield HCCS ((sup 2)II)) and C2H3S ((sup 2)A')). Substantial barriers were found in the exit channels for every combination of method and basis set considered in this work, which effectively precludes hydrogen elimination pathways for both S + C2H2 and S + C2H4 in the ultracold interstellar medium where only very modest barriers can be surmounted and processes without barriers tend to predominate. However, if one or both intermediates is formed and stabilized efficiently under cometary or dense interstellar cloud conditions, they could serve as temporary reservoirs for S atom and participate in reactions such as S + C2H2S (right arrow) S2 = C2H2 or S + C2H4S (right arrow) S2 + C2H4. For formation and stabilization to be efficient, the reaction must possess a barrier height small enough to be surmountable at low temperatures yet large enough to prevent redissociation to reactants. Barrier heights computed with B3LYP and large basis sets are very low, but more rigorous QCISD(T) and RCCSD(T) results indicate that the barrier heights are closer to 3-4 kcal/mol. The calculations therefore indicate that S + C2H2 or S + C2H4 could contribute to the formation of S2 in comets and may serve as a means to gauge coma temperature. The energetics of the ethylene reaction are more favorable.

Woon, David E.↗
NASA NTRS1992

Photon number squeezed states in semiconductor lasers

Electromagnetic fields, with the noise on one quadrature component reduced to below the quantum mechanical zero-point fluctuation level and the noise on the other quadrature component enhanced to above it, are currently of great interest in quantum optics because of their potential applications to various precision measurements. Such squeezed states of light are usually produced by imposing nonlinear unitary evolution on coherent (or vacuum) states. On the other hand, squeezed states with reduced photon number noise and enhanced phase noise are generated directly by a constant current-driven semiconductor laser. This is the simplest scheme for the generation of nonclassical light, and so far it has yielded the largest quantum noise reduction. The mutual coupling between a lasing junction and an external electrical circuit provides opportunities for exploring the macroscopic and microscopic quantum effects in open systems.

Yamamoto, Yoshihisa↗
NASA NTRS1979

The photolysis of chlorine in the presence of ozone, nitric acid and nitrogen dioxide

The following three systems were investigated: the Cl2-O3 system, the Cl2-O2-NO system and the Cl2-NO2-M system. In the first system, the reaction between ClO and O3, the reaction between OClO and O3, and the mechanism of the Cl2-O3 system were studied. In the second system, the reaction between ClOO and NO was investigated. In the last system, the reaction between Cl and NO2 was investigated as well as the kinetics of the chemiluminescence of the Cl-NO2-O3 reaction. In the first system, Cl2 was photolyzed at 366 nm in the presence of O3 within the temperature range 254-297 K. O3 was removed with quantum yields of 5.8 + or - 0.5, 4.0 + or - 0.3, 2.9 + or - 0.3 and 1.9 + or - 0.2 at 297, 283, 273, and 252 K respectively, invariant to changes in the initial O3 or Cl2 concentration, the extent of conversion or the absorbed intensity, I sub a. The addition of nitrogen had no effect on -phi(03). The Cl2 removal quantum yields were 0.11 + or - 0.02 at 297 K for Cl2 conversions of about 30%, much higher than expected from mass balance considerations based on the initial quantum yield of 0.089 + or - 0.013 for OClO formation at 297 K. The final chlorine-containing product was Cl2O7. It was produced at least in part through the formation of OClO as an intermediate which was also observed with an initial quantum yield of phi sub i(OClO) = 2500 exp(-(3025 + or - 625)/T) independent of (O3) or I sub a.

Stuper, W. W.↗
NASA NTRS1990

Interfacial wave theory of dendrite growth - Global mode solution and quantum condition

The signal feedback process at the edge of the dendrite tip is investigated, and the global instability mechanism of the system is derived. A mechanism is developed to describe a discrete set of unstable global modes for the system. Called WEASR, the method considers the wave emission at the turning point and signal reflections between the turning point and the front edge of the tip. It is shown that the method can obtain the asymptotic solutions for the unstable global modes and the quantum condition for the corresponding eigenvalues. A turning point called the pattern formation condition is shown to be crucial in the formation of dendritic structure and the choice of the final tip velocity. The wave emission process is outlined, and the importance of a signal feedback process at the edge of the dendrite tip is demonstrated. Parameters such as stability and surface tension can be analyzed in terms of their effects on WEASR modes.

Xu, Jian-Jun↗
NASA NTRS1997

Formation of Carbon Nanotube Based Gears: Quantum Chemistry and Molecular Mechanics Study of the Electrophilic Addition of o-Benzyne to Fullerenes, Graphene, and Nanotubes

Considerable progress has been made in recent years in chemical functionalization of fullerene molecules. In some cases, the predominant reaction products are different from those obtained (using the same reactants) from polycyclic aromatic hydrocarbons (PAHs). One such example is the cycloaddition of o-benzyne to C60. It is well established that benzyne adds across one of the rings in naphthalene, anthracene and other PAHs forming the [2+4] cycloaddition product (benzobicyclo[2.2.2.]-octatriene with naphthalene and triptycene with anthracene). However, Hoke et al demonstrated that the only reaction path for o-benzyne with C60 leads to the [2+2] cycloaddition product in which benzyne adds across one of the interpentagonal bonds (forming a cyclobutene ring in the process). Either reaction product results in a loss of aromaticity and distortion of the PAH or fullerene substrate, and in a loss of strain in the benzyne. It is not clear, however, why different products are preferred in these cases. In the current paper, we consider the stability of benzyne-nanotube adducts and the ability of Brenner's potential energy model to describe the structure and stability of these adducts. The Brenner potential has been widely used for describing diamondoid and graphitic carbon. Recently it has also been used for molecular mechanics and molecular dynamics simulations of fullerenes and nanotubes. However, it has not been tested for the case of functionalized fullerenes (especially with highly strained geometries). We use the Brenner potential for our companion nanogear simulations and believe that it should be calibrated to insure that those simulations are physically reasonable. In the present work, Density Functional theory (DFT) calculations are used to determine the preferred geometric structures and energetics for this calibration. The DFT method is a kind of ab initio quantum chemistry method for determining the electronic structure of molecules. For a given basis set expansion, it is comparable in accuracy to the MP2 method (better than Hartree Fock, but less accurate than more extensive electron correlation methods such as MP4 or CCSD). However, for systems with large numbers of basis functions it more efficient than any other methods that include electron correlation effects. In this presentation we show the results of DFT calculations for the reaction of benzyne with naphthalene, C60, and nanotube models. We compare energies for [2+2] and [2+4] cycloaddition products. The preferred products for the naphthalene and C60 reactions have been determined by experiment and, thus, these cases serve as a validation of our quantum chemical approach. We also compare the DFT and Brenner potential results. Finally we can predict the likelihood of reaction between benzyne and nanotubes.

Jaffe, Richard↗
NASA NTRS2000

2D Quantum Mechanical Study of Nanoscale MOSFETs

With the onset of quantum confinement in the inversion layer in nanoscale MOSFETs, behavior of the resonant level inevitably determines all device characteristics. While most classical device simulators take quantization into account in some simplified manner, the important details of electrostatics are missing. Our work addresses this shortcoming and provides: (a) a framework to quantitatively explore device physics issues such as the source-drain and gate leakage currents, DIBL, and threshold voltage shift due to quantization, and b) a means of benchmarking quantum corrections to semiclassical models (such as density-gradient and quantum-corrected MEDICI). We have developed physical approximations and computer code capable of realistically simulating 2-D nanoscale transistors, using the non-equilibrium Green's function (NEGF) method. This is the most accurate full quantum model yet applied to 2-D device simulation. Open boundary conditions and oxide tunneling are treated on an equal footing. Electrons in the ellipsoids of the conduction band are treated within the anisotropic effective mass approximation. We present the results of our simulations of MIT 25, 50 and 90 nm "well-tempered" MOSFETs and compare them to those of classical and quantum corrected models. The important feature of quantum model is smaller slope of Id-Vg curve and consequently higher threshold voltage. Surprisingly, the self-consistent potential profile shows lower injection barrier in the channel in quantum case. These results are qualitatively consistent with ID Schroedinger-Poisson calculations. The effect of gate length on gate-oxide leakage and subthreshold current has been studied. The shorter gate length device has an order of magnitude smaller current at zero gate bias than the longer gate length device without a significant trade-off in on-current. This should be a device design consideration.

Svizhenko, Alexei↗
NASA NTRS2003

Competing Classical and Quantum Effects in Shape Relaxation of a Metallic Nanostructure

We demonstrate for the first time that the quantum size effect (QSE) plays a competing role along side the classical thermodynamic effect in the shape relaxation of a small metallic island. Together, these effects transforms a lead(Pb) island grown on Si(111) substrate from its initially flattop faceted morphology to a peculiar ring-shape island, a process catalysed by the tip electric field of a scanning tunnelling microscope (STM). We shall show for the first time how QSE affects the relaxation process dynamically. In particular, it leads to a novel strip-flow growth and double-step growth on selective strips of a plateau inside the ring, defined by the substrate steps more than 60?0?3 below. It appears that atoms diffusing on the plateau can clearly (sub i)(deg)sense(sub i)+/- the quantized energy states inside the island and have preferentially attached to regions that further reduces the surface energy as a result of the QSE, limiting its own growth and stabilizing the ring shape. The mechanism proposed here offers a sound explanation for ring shape metal and semiconductor islands observed in other systems as well.

Chen, Dongmin↗
NASA NTRS2002

Limits on the UV Photodecomposition of Carbonates on Mars

The effect of UV (ultraviolet) light on the stability of calcium carbonate in a simulated martian atmosphere was experimentally investigated. Sample cells containing C-13 labeled calcite were irradiated with a Xe arc lamp in 10 mbar of simulated martian atmosphere and a quadrupole mass spectrometer was used to monitor the headspace gases for the production of (13)CO2. We found no experimental evidence of the UV photodecomposition of calcium carbonate in a simulated martian atmosphere. Extrapolating the lower limit of detection of our experimental system to an upper limit of carbonate decomposition on Mars yields a quantum efficiency of 3.5 x 10(exp -8) molecules/photon over the wavelength interval of 190-390 nm and a maximum UV photodecomposition rate of 1.2 x 10(exp -13) kg m(exp -2) s(exp -1) from a calcite surface. The maximum loss of bulk calcite due to this process would be 2.5 nm yr(exp -1). However, calcite is expected to be thermodynamically stable on the surface of Mars and potential UV photodecomposition reaction mechanisms indicate that while calcium carbonate may decompose under vacuum, it would be stable in a CO2 atmosphere. Given the expected stability of carbonate on Mars and our inability to detect carbonate decomposition, we conclude that it is unlikely that the apparent absence of carbonate on the martian surface is due to UV photo decomposition of calcite in the current environment.

Quinn, Richard↗
NASA NTRS2004

Deriving Laws from Ordering Relations

The effect of Richard T. Cox's contribution to probability theory was to generalize Boolean implication among logical statements to degrees of implication, which are manipulated using rules derived from consistency with Boolean algebra. These rules are known as the sum rule, the product rule and Bayes Theorem, and the measure resulting from this generalization is probability. In this paper, I will describe how Cox s technique can be further generalized to include other algebras and hence other problems in science and mathematics. The result is a methodology that can be used to generalize an algebra to a calculus by relying on consistency with order theory to derive the laws of the calculus. My goals are to clear up the mysteries as to why the same basic structure found in probability theory appears in other contexts, to better understand the foundations of probability theory, and to extend these ideas to other areas by developing new mathematics and new physics. The relevance of this methodology will be demonstrated using examples from probability theory, number theory, geometry, information theory, and quantum mechanics.

Knuth, Kevin H.↗
NASA NTRS2003

Self-Supervised Dynamical Systems

Some progress has been made in a continuing effort to develop mathematical models of the behaviors of multi-agent systems known in biology, economics, and sociology (e.g., systems ranging from single or a few biomolecules to many interacting higher organisms). Living systems can be characterized by nonlinear evolution of probability distributions over different possible choices of the next steps in their motions. One of the main challenges in mathematical modeling of living systems is to distinguish between random walks of purely physical origin (for instance, Brownian motions) and those of biological origin. Following a line of reasoning from prior research, it has been assumed, in the present development, that a biological random walk can be represented by a nonlinear mathematical model that represents coupled mental and motor dynamics incorporating the psychological concept of reflection or self-image. The nonlinear dynamics impart the lifelike ability to behave in ways and to exhibit patterns that depart from thermodynamic equilibrium. Reflection or self-image has traditionally been recognized as a basic element of intelligence. The nonlinear mathematical models of the present development are denoted self-supervised dynamical systems. They include (1) equations of classical dynamics, including random components caused by uncertainties in initial conditions and by Langevin forces, coupled with (2) the corresponding Liouville or Fokker-Planck equations that describe the evolutions of probability densities that represent the uncertainties. The coupling is effected by fictitious information-based forces, denoted supervising forces, composed of probability densities and functionals thereof. The equations of classical mechanics represent motor dynamics that is, dynamics in the traditional sense, signifying Newton s equations of motion. The evolution of the probability densities represents mental dynamics or self-image. Then the interaction between the physical and metal aspects of a monad is implemented by feedback from mental to motor dynamics, as represented by the aforementioned fictitious forces. This feedback is what makes the evolution of probability densities nonlinear. The deviation from linear evolution can be characterized, in a sense, as an expression of free will. It has been demonstrated that probability densities can approach prescribed attractors while exhibiting such patterns as shock waves, solitons, and chaos in probability space. The concept of self-supervised dynamical systems has been considered for application to diverse phenomena, including information-based neural networks, cooperation, competition, deception, games, and control of chaos. In addition, a formal similarity between the mathematical structures of self-supervised dynamical systems and of quantum-mechanical systems has been investigated.

Zak, Michail↗
NASA NTRS1989

A high level Ab initio study of the anionic hydrogen-bonded complexes FH-CN-, FH-NC-, H2O-CN- and H2O-NC-

HF, H2O, CN- and their hydrogen-bonded complexes were studied using state-of-the-art ab initio quantum mechanical methods. A large Gaussian one particle basis set consisting of triple zeta plus double polarization plus diffuse s and p functions (TZ2P + diffuse) was used. The theoretical methods employed include self consistent field, second order Moller-Plesset perturbation theory, singles and doubles configuration interaction theory and the singles and doubles coupled cluster approach. The FH-CN- and FH-NC- and H2O-CN-, H2O-NC- pairs of complexes are found to be essentially isoenergetic. The first pair of complexes are predicted to be bound by approx. 24 kcal/mole and the latter pair bound by approximately 15 kcal/mole. The ab initio binding energies are in good agreement with the experimental values. The two being shorter than the analogous C-N hydrogen bond. The infrared (IR) spectra of the two pairs of complexes are also very similar, though a severe perturbation of the potential energy surface by proton exchange means that the accurate prediction of the band center of the most intense IR mode requires a high level of electronic structure theory as well as a complete treatment of anharmonic effects. The bonding of anionic hydrogen-bonded complexes is discussed and contrasted with that of neutral hydrogen-bonded complexes.

Lee, Timothy J.↗
NASA NTRS1989

A high-level ab initio study of the anionic hydrogen-bonded complexes FH-CN(-), FH-NC(-), H2O-CN(-), and H2O-NC(-)

HF, H2O, CN- and their hydrogen-bonded complexes were studied using state-of-the-art ab initio quantum mechanical methods. A large Gaussian one particle basis set consisting of triple zeta plus double polarization plus diffuse s and p functions (TZ2P + diffuse) was used. The theoretical methods employed include self consistent field, second order Moller-Plesset perturbation theory, singles and doubles configuration interaction theory and the singles and doubles coupled cluster approach. The FH-CN- and FH-NC- and H2O-CN-, H2O-NC- pairs of complexes are found to be essentially isoenergetic. The first pair of complexes are predicted to be bound by approx. 24 kcal/mole and the latter pair bound by approximately 15 kcal/mole. The ab initio binding energies are in good agreement with the experimental values. The two being shorter than the analogous C-N hydrogen bond. The infrared (IR) spectra of the two pairs of complexes are also very similar, though a severe perturbation of the potential energy surface by proton exchange means that the accurate prediction of the band center of the most intense IR mode requires a high level of electronic structure theory as well as a complete treatment of anharmonic effects. The bonding of anionic hydrogen-bonded complexes is discussed and contrasted with that of neutral hydrogen-bonded complexes.

Lee, Timothy J.↗
NASA NTRS1991

Recent advances in the ITO/InP solar cell

It was demonstrated that Indium Tin Oxide (ITO)/InP solar cells can now be made on as-received p(-) bulk substrates which are of nearly equal quality to those which could previously only be made on epitaxially grown p(-) InP base layers. Although this advancement is due in part to both increases in substrate quality and a better understanding of back contact formation, it appears that the passivation/compensation effects resulting from having H2 in the sputtering gas tends to reduce significantly the performance differences previously observed between these two substrates. It is shown that since high efficiency ITO/InP cells can be made from as-received substrates, and since the type conversion process is not highly spatially dependent, large area ITO/InP cells (4 sq cm) with efficiencies approaching 17 percent (Global) can be made. Furthermore, the measured open circuit voltages (V sub OC) and quantum efficiencies (QEs) from these large cells suggest that, when they are processed using optimum grid designs, the efficiencies will be nearly equal to that of the smaller cells thus far produced. It has been shown, through comparative experiments involving ITO/InP and IO/InP cells, that Sn may not be the major cause of type conversion of the InP surface and thus further implies that the ITO may not be an essential element in this type of device. Specifically, very efficient photovoltaic solar cells were made by sputtering (Sn free) In2O3 showing that type conversion and subsequent junction formation will occur even in the absence of the sputtered SN species. The result suggests that sputter damage may indeed be the important mechanism(s) of type conversion. Finally, an initial study of the stability of the ITO/InP cell done over the course of about one year has indicated that the J(sub SC) (short circuit current) and the fill factor (FF) are measurably stable within experimental certainty.

Gessert, T. A.↗
NASA NTRS1995

Boson localization and universality in YBa2Cu(3-x)M(x)O(7-delta)

We consider a two component mixture of charged fermions on neutralizing background with all sign combinations and arbitrarily small mass ratios. In the two impurity limit for the heavier component we show that the pair forms a bound state for all charge combinations. In the lowest order approximation we derive a closed form expression Veff(r) for the binding potential which has short-range repulsion followed by attraction. In the classical limit, when the mass of embedded particles is large m2 much greater than m, we can calculate from Veff(r) also the cohesive energy E and the bond length R of a metallic crystal such as lithium. The lowest order result is R = 3.1 A, E = -0.9 eV, not entirely different from the experimental result for lithium metal. The same interaction for two holes on a parabolic band with m2 greater than m gives the quantum mechanical bound state which one may interpret as a boson or local pair in the case of high-Te and heavy fermion superconductors. We also show that for compounds of the type YBa2Cu(3 - x)M(x)O(7 - delta) one can understand most of the experimental results for the superconducting and normal states with a single temperature dependent boson breaking function f(T) for each impurity content x governing the decay of bosons into pairing fermions. In the normal state f(T) turns out to be a linear, universal function, independent of the impurity content I and the oxygen content delta. We predict with universality a depression in Tc(x) with slight down bending in agreement with experiment. As a natural consequence of the model the bosons become localized slightly above Tc due to the Wigner crystallization, enhanced with lattice local field minima. The holes remain delocalized with a linearly increasing concentration in the normal state, thus explaining the rising Hall density. The boson localization temperature T(sub BL) shows up as a minimum in the Hall density R(sub ab)(exp -1). We also give explanation for very recently observed scaling of temperature dependent Hall effect in La(2 - x)Sr(x)CuO4.

Kallio, A.↗
NASA NTRSDate not supplied

REACTER 2.0: Quantum-Informed Reaction Constraints and Automated Interaction Typing

REACTER is a heuristic method for modeling chemical reactions in classical molecular dynamics simulations, implemented in LAMMPS as fix bond/react. The authors recently extended LAMMPS to support alphanumeric labels for atom types, bond types etc., which enables the pre- and post-reaction templates required by the REACTER protocol to be portable between different simulations and greatly simplifies the task of creating simulation-ready reaction templates. To further increase the generality of reaction templates, support for wildcard characters within atom types has been added, along with the automatic assignment of interaction types for new bonds, angles, etc. based on the involved atom types. In some cases, this feature can express a class of reactions with one pair of reaction templates, where previously dozens may have been required. Advanced reaction constraints have also been added, including an Arrhenius constraint to enforce an effective activation energy, a root-mean-square-deviation option for complex geometrical constraints, as well as a custom constraint that leverages LAMMPS’ powerful built-in variable framework. Other new features include variable support for various inputs (e.g., to allow reaction rates or cutoffs to be dependent on overall conversion), on-the-fly update of molecule IDs, and the ability to create new atoms positioned with respect to the reaction site. The new features are applied to modeling polymeric, thermosetting and composite materials, and advanced applications of the new reaction constraints are demonstrated. For example, REACTER is shown to accurately reproduce mechanically-induced bond breaking, as characterized by third-order DFT-based tight-binding (DFTB3) simulations, via a constraint on the total potential energy of the involved atoms.

polymer simulations↗
NASA NTRS1997

Machine Phase Fullerene Nanotechnology: 1996

NASA has used exotic materials for spacecraft and experimental aircraft to good effect for many decades. In spite of many advances, transportation to space still costs about $10,000 per pound. Drexler has proposed a hypothetical nanotechnology based on diamond and investigated the properties of such molecular systems. These studies and others suggest enormous potential for aerospace systems. Unfortunately, methods to realize diamonoid nanotechnology are at best highly speculative. Recent computational efforts at NASA Ames Research Center and computation and experiment elsewhere suggest that a nanotechnology of machine phase functionalized fullerenes may be synthetically relatively accessible and of great aerospace interest. Machine phase materials are (hypothetical) materials consisting entirely or in large part of microscopic machines. In a sense, most living matter fits this definition. To begin investigation of fullerene nanotechnology, we used molecular dynamics to study the properties of carbon nanotube based gears and gear/shaft configurations. Experiments on C60 and quantum calculations suggest that benzyne may react with carbon nanotubes to form gear teeth. Han has computationally demonstrated that molecular gears fashioned from (14,0) single-walled carbon nanotubes and benzyne teeth should operate well at 50-100 gigahertz. Results suggest that rotation can be converted to rotating or linear motion, and linear motion may be converted into rotation. Preliminary results suggest that these mechanical systems can be cooled by a helium atmosphere. Furthermore, Deepak has successfully simulated using helical electric fields generated by a laser to power fullerene gears once a positive and negative charge have been added to form a dipole. Even with mechanical motion, cooling, and power; creating a viable nanotechnology requires support structures, computer control, a system architecture, a variety of components, and some approach to manufacture. Additional information is contained within the original extended abstract.

Globus, Al↗
NASA NTRS1996

Macroscopic Violation of Three Cauchy-Schwarz Inequalities Using Correlated Light Beams From an Infra-Red Emitting Semiconductor Diode Array

We briefly review quantum mechanical and semi-classical descriptions of experiments which demonstrate the macroscopic violation of the three Cauchy-Schwarz inequalities: g(sup 2)(sub 11)(0) greater than or equal to 1; g(sup 2)(sub 11)(0) greater than or equal to g(sup 2)(sub 11)(t), (t approaches infinity); (the absolute value of g(sup 2)(sub 11)(0))(exp 2) less than or equal to g(sup 2)(sub 11)(0) g(sup 2)(sub 11)(0). Our measurements demonstrate the violation, at macroscopic intensities, of each of these inequalities. We show that their violation, although weak, can be demonstrated through photodetector current covariance measurements on correlated sub-Poissonian Poissonian, and super Poissonian light beams. Such beams are readily generated by a tandem array of infrared-emitting semiconductor junction diodes. Our measurements utilize an electrically coupled array of one or more infrared-emitting diodes, optically coupled to a detector array. The emitting array is operated in such a way as to generate highly correlated beams of variable photon Fano Factor. Because the measurements are made on time scales long compared with the first order coherence time and with detector areas large compared with the corresponding coherence areas, first order interference effects are negligible. The first and second inequalities are violated, as expected, when a sub-Poissonian light beam is split and the intensity fluctuations of the two split beams are measured by two photodetectors and subsequently cross-correlated. The third inequality is violated by bunched (as well as anti-bunched) beams of equal intensity provided the measured cross correlation coefficient exceeds (F - 1)/F, where F is the measured Fano Factor of each beam. We also investigate the violation for the case of unequal beams.

Edwards, P. J.↗