Effect of polarization on population transfer in H2 by stimulated Raman transition with partially overlapping laser pulses

Polarization effects on population transfer by stimulated Raman transition using overlapping time dependent pump and Stokes laser pulses from the ground X ¹Σ _g ^/+ (v _g=0, J _g=1) level of H₂ to the final X ¹Σ _g ^/+ (v _f=1, J _f=1) level via the intermediate B ¹Σ _u ^/+ (v _i=14, J _i=0,2), C ¹Π _u ^/+ (v _i=3, J _i=2) and C ¹Π _u ^/− (v _i=3, J _i=1) levels have been theoretically investigated by applying the density matrix formalism. We have studied in detail the dependence of the population transfer on time delay between two pulses for the cases of on-resonance excitations considering linear parallel and same-sense circular polarizations of the fields. The pump and Stokes fields are taken as having Gaussian pulse shapes with peak intensities I _P ^/0 (I _S ^/0 )=2 × 10⁶ and 1 × 10⁷ W/cm². Density matrix equations have been solved for each value of the magnetic quantum number M _g(0, ±1) of the initial ground level taking into account the M _g dependence of the Rabi frequencies. M _g — averaged population transfer to the final level has also been calculated. For resonance excitations to the B(14, 0) or C(3, 1) levels, appreciable population transfer is achieved for intuitive pulse order for some particular values of M _g and M _i (magnetic quantum number of the resonant intermediate level) depending on the nature of polarizations. The calculated values of M _g — averaged population transfer for the two cases of polarizations show that for on-resonance excitation to the B(14, 0) or the C(3, 1) level, linear parallel polarization of the laser fields yield more transfer efficiency whereas for resonance excitation to the B(14, 2) level, larger population transfer results from the same-sense circular polarizations. For resonance excitation to the C(3, 2) level, M _g — averaged population is found to be almost polarization independent. The calculations for the six-level H₂ system reveal some interesting features of polarization effects on the population transfer efficiency.     

THE HADAMARD INEQUALITY FOR CONVEX FUNCTION VIA FRACTIONAL INTEGRALS

In this paper, we establish several inequalities for some differantiable mappings that are connected with the Riemann-Liouville fractional integrals. The analysis used in the proofs is fairly elementar...     

Stepwise fluorescence changes of quantum dots: single-molecule spectroscopic studies on the properties of turn-on quantum dots

Single-molecule spectroscopy of turn-on quantum dots induced by NADPH-dependent biocatalyzed transformations reveals that the fluorescence intensities of quantum dots functionalized with Nile Blue are stepwisely and reversibly changed in the presence of NADPH.     

A Facile Synthesis of Diethyl 1-Formylalkane Phosphonates via Ozonolysis of 1-Alkyl Allylic Phosphonates

The 1-formylalkanephosphonates were obtained by the ozonolysis of the corresponding 1-alkylated allylphosphonates, which had been previously prepared by treatment with n-BuLi, followed by addition of alkyl halides.     

Rough Isometry and <Emphasis Type="Italic">p</Emphasis>-Harmonic Boundaries of Complete Riemannian Manifolds

In this paper, we describe the behavior of bounded energy finite solutions for certain nonlinear elliptic operators on a complete Riemannian manifold in terms of its p-harmonic boundary. We also prove that if two complete Riemannian manifolds are roughly isometric to each other, then their p-harmonic boundaries are homeomorphic to each other. In the case, there is a one to one correspondence between the sets of bounded energy finite solutions on such manifolds. In particular, in the case of the Laplacian, it becomes a linear isomorphism between the spaces of bounded harmonic functions with finite Dirichlet integral on the manifolds. This work was supported by grant No. R06-2002-012-01001-0(2002) from the Basic Research Program of the Korea Science & Engineering Foundation.     

THE SINGULARLY PERTURBED NONLOCAL REACTION DIFFUSION SYSTEM

In this paper the singularly perturbed initial boundary value problems for the nonlocal reaction diffusion system are considered. Unsing the iteration method and the comparison theorem, the existence, uniqueness and its asymptotic behavior of solution for the problem are studied.     

Effect of substitution of Ce on superconducting properties of Bi1.7Pb0.3Sr2Ca2−x Ce x Cu3O10+δ system

We have investigated the superconducting properties of the Bi_1.7 Pb_0.3Sr₂Ca_2−xCe _x Cu₃O_10+δ system with x=0.00, 0.02, 0.04, 0.08 and 0.1 by X-ray diffraction and magnetic susceptibility. The substitution of Ce for Ca has been found to drastically change the superconducting properties of the system. X-ray diffraction studies on these compounds indicate decrease in the c-parameter with increased substitution of Ce at Ca site and volume fraction of high T _c (2 : 2 : 2 : 3) phase decreases and low T _c phase increases. The magnetic susceptibility of this compound shows that the diamagnetic on set superconducting transition temperature (onset) varies from 109 K to 51 K for x=0.00, 0.02, 0.04, 0.08 and 0.1. These results suggest the possible existence of Ce in a tetravalent state rather than a trivalent state in this system; that is, Ca²⁺ → Ce⁴⁺ replacement changes the hole carrier concentration. Hole filling is the cause of lowering T _c of the system.     

High spin spectroscopy of 139Pr

The high spin states in N=80 ¹³⁹Pr have been investigated by in-beam γ-spectroscopic techniques following the reaction ¹³⁰Te (¹⁴N, 5n) reaction at E=75 MeV, using a gamma detector array, consisting of seven 23% compton-suppressed high purity germanium detectors and a multiplicity ball of fourteen bismuth germanate elements. Based on γ-γ coincidence data, the level scheme of ¹³⁹Pr has been considerably extended up to 7.2 MeV excitation. Tentative spin-parity assignments are done for the newly proposed levels on the basis of the DCO ratios corresponding to strong gates and the available information from the earlier light ion experiments.     

Nonnegative solutions of an elliptic equation and Harnack ends of Riemannian manifolds

In this paper, we give a barrier argument at infinity for solutions of an elliptic equation on a complete Riemannian manifold. By using the barrier argument, we can construct a nonnegative (bounded, respectively) solution of the elliptic equation, which takes the given data at infinity of each end. In particular, we prove that if a complete Riemannian manifold has finitely many ends, each of which is Harnack and nonparabolic, then the set of bounded solutions of the elliptic equation is finite dimensional, in some sense. We also prove that if a complete Riemannian manifold is roughly isometric to a complete Riemannian manifold satisfying the volume doubling condition, the Poincaré inequality and the finite covering condition on each end, then there exists a nonnegative solution of an elliptic equation taking the given data at infinity of each end of the manifold. These results generalize those of Yau, of Donnelly, of Grigor'yan, of Li and Tam, of Holopainen, and of the present authors, but with the barrier argument at infinity that enables one to overcome the obstacle due to the nonlinearity of solutions. Received: 11 November 1999