Analysis of adiabatic transfer in cavity quantum electrodynamics

A three-level atom in a Λ configuration trapped in an optical cavity forms a basic unit in a number of proposed protocols for quantum information processing. This system allows for efficient storage of cavity photons into long-lived atomic excitations, and their retrieval with high fidelity, in an adiabatic transfer process through the ‘dark state’ by a slow variation of the control laser intensity. We study the full quantum mechanics of this transfer process with a view to examine the non-adiabatic effects arising from inevitable excitations of the system to states involving the upper level of Λ, which is radiative. We find that the fidelity of storage is better, the stronger the control field and the slower the rate of its switching off. On the contrary, unlike the adiabatic notion, retrieval is better with faster rates of switching on of an optimal control field. Also, for retrieval, the behaviour with dissipation is non-monotonic. These results lend themselves to experimental tests. Our exact computations, when applied to slow variations of the control intensity for strong atom–photon couplings, are in very good agreement with Berry’s superadiabatic transfer results without dissipation.     

Study of neutron-rich Mo isotopes by the projected shell model approach

The projected shell model (PSM) calculations have been performed for the neutron-rich even–even ^102?110Mo and odd—even ^103?109Mo isotopes. The present calculation reproduces the available experimental data on the yrast bands. In case of even–even nuclei, the structure of yrast bands is analysed and electromagnetic quantities are compared with the available experimental data. The g-factors have been predicted for high spin states. For the odd-neutron nuclei, the structures of yrast positive- and negative-parity bands are analysed and found to be in reasonable agreement with the experiments for ^103?107Mo. The disagreement of the calculated and observed plots for energy staggering quantity clearly establishes the occurrence of sizable triaxiality in ^103,105Mo and also predicts a decrease in the quantum of triaxiality with increasing neutron number and angular momentum for odd mass neutron-rich Mo isotopes.     

Laser-assisted surface cleaning of metallic components

Removal of a thin oxide layer from a tungsten ribbon and ThO₂ particulates from zircaloy surface was achieved using a pulsed Nd:YAG laser. The removal mechanism of the oxide layer from the tungsten ribbon was identified as spallation or sublimation depending on the wavelength and fluence of the coherent radiation. The oxidized and cleaned surfaces were analysed by scanning electron microscopy (SEM), energy dispersive X-ray analysis (EDS) and atomic force microscopy (AFM). Laser-cleaned tungsten ribbons were used in a thermal ionization mass spectrometer (TIMS) to determine isotopic composition of neodymium atoms. The fundamental (1064 nm) and the third harmonic (355 nm) radiations were found to be the most effective in removing ThO₂ particulates from the zircaloy surface. Decontamination efficiency was found to be critically dependent on the wavelength of the coherent radiation and number of exposures. The mechanism of cleaning of ThO₂ particulates from the zircaloy surface at different wavelengths of the incident radiation has been explained qualitatively.     

A SURVEY OF THE ADDITIVE EIGENVALUE PROBLEM (WITH APPENDIX BY M. KAPOVICH)

The classical Hermitian eigenvalue problem addresses the following question: What are the possible eigenvalues of the sum A + B of two Hermitian matrices A and B, provided we fix the eigenvalues of A and B. A systematic study of this problem was initiated by H. Weyl (1912). By virtue of contributions from a long list of mathematicians, notably Weyl (1912), Horn (1962), Klyachko (1998) and Knutson–Tao (1999), the problem is finally settled. The solution asserts that the eigenvalues of A + B are given in terms of certain system of linear inequalities in the eigenvalues of A and B. These inequalities (called the Hom inequalities) are given explicitly in terms of certain triples of Schubert classes in the singular cohomology of Grassmannians and the standard cup product. Belkale (2001) gave a smaller set of inequalities for the problem in this case (which was shown to be optimal by Knutson–Tao–Woodward). The Hermitian eigenvalue problem has been extended by Berenstein–Sjamaar (2000) and Kapovich–Leeb–Millson (2009) for any semisimple complex algebraic group G. Their solution is again in terms of a system of linear inequalities obtained from certain triples of Schubert classes in the singular cohomology of the partial ag varieties G/P (P being a maximal parabolic subgroup) and the standard cup product. However, their solution is far from being optimal. In a joint work with P. Belkale, we define a deformation of the cup product in the cohomology of G/P and use this new product to generate our system of inequalities which solves the problem for any G optimally (as shown by Ressayre). This article is a survey (with more or less complete proofs) of this additive eigenvalue problem. The eigenvalue problem is equivalent to the saturated tensor product problem. We also give an extension of the saturated tensor product problem to the saturated restriction problem for any pair G ? ? of connected reductive algebraic groups. In the appendix by M. Kapovich, a connection between metric geometry and the representation theory of complex semisimple algebraic groups is explained. The connection runs through the theory of buildings. This connection is exploited to give a uniform (though not optimal) saturation factor for any G.     

Mechanistic Aspects of Ligand Substitution on the Hydroxopentaaquarhodium(III) Ion in Aqueous Solution by Sulfur‐Containing Bioactive Ligands

The kinetics of the interactions between three sulfur‐containing ligands, thioglycolic acid, 2‐thiouracil, glutathione, and the title complex, have been studied spectrophotometrically in aqueous medium as a function of the concentrations of the ligands, temperature, and pH at constant ionic strength. The reactions follow a two‐step process in which the first step is ligand‐dependent and the second step is ligand‐independent chelation. Rate constants (k₁ ～10^?3 s^?1 and k₂ ～10^?5 s^?1) and activation parameters (for thioglycolic acid: ΔH₁^≠ = 22.4 ± 3.0 kJ mol^?1, ΔS₁^≠ = ?220 ± 11 J K^?1 mol^?1, ΔH₂^≠ = 38.5 ± 1.3 kJ mol^?1, ΔS₂^≠ = ?204 ± 4 J K^?1 mol^?1; for 2‐thiouracil: ΔH₁^≠ = 42.2 ± 2.0 kJ mol^?1, ΔS₁^≠ = ?169 ± 6 J K^?1 mol^?1, ΔH₂^≠ = 66.1 ± 0.5 kJ mol^?1, ΔS₂^≠ = ?124 ± 2 J K^?1 mol^?1; for glutathione: ΔH₁^≠ = 47.2 ± 1.7 kJ mol^?1, ΔS₁^≠ = ?155 ± 5 J K^?1mol^?1, ΔH₂^≠ = 73.5 ± 1.1 kJ mol^?1, ΔS₂^≠ = ?105 ± 3 J K^?1 mol^?1) were calculated. Based on the kinetic and activation parameters, an associative interchange mechanism is proposed for the interaction processes. The products of the reactions have been characterized from IR and ESI mass spectroscopic analysis. A rate law involving the outer sphere association complex formation has been established as      

Synthesis of Dinaphtho-dioxaphosphepin-4-oxides, Epoxides and Bisphosphonates

A few new seven-membered phosphorus heterocyclic compounds and bis-phosphonates (5a—5g, 5f’, 5g’, 9 and 10) were prepared by the reaction of 4-bromo dioxaphosphepin (2) with various Grignard reagents followed by their oxidation with H2O2. All the compounds were thoroughly characterized by elemental analysis, IR, 1H, 13C, 31P NMR and mass spectral data. Their antimicrobial activity was evaluated and some of them possess significant activity.