Narrow-band N-resonance formed in thin rubidium atomic layers

The narrow-band N-resonance formed in a ?? system of D ₁-line rubidium atoms is studied in the presence of a buffer gas (neon) and the radiations of two continuous narrow-band diode lasers. Special-purpose cells are used to investigate the dependence of the process on vapor column thickness L in millimeter, micrometer, and nanometer ranges. A comparison of the dependences of the N-resonance and the electromagnetically induced transparency (EIT) resonance on L demonstrates that the minimum (record) thickness at which the N-resonance can be detected is L = 50 ??m and that a high-contrast EIT resonance can easily be formed even at L ?? 800 nm. The N-resonance in a magnetic field for ⁸⁵Rb atoms is shown to split into five or six components depending on the magnetic field and laser radiation directions. The results obtained indicate that levels F _g = 2, 3 are initial and final in the N-resonance formation. The dependence of the N-resonance on the angle between the laser beams is analyzed, and practical applications are noted.     

Circular Dichroism of Atomic Transitions of the Rb D1 Line in Magnetic Fields

Optics and Spectroscopy - The circular dichroism effect has been investigated for atomic transitions of the Rb D1 line in magnetic fields of up to 3 kG using circularly polarized σ+ and...     

Square principles in ℙ<Subscript>max</Subscript> extensions

By forcing with P_max over strong models of determinacy, we obtain models where different square principles at ω ₂ and ω ₃ fail. In particular, we obtain a model of \({2^{{\aleph _0}}} = {2^{{\aleph _1}}} = {\aleph _2} + {\neg }\square \left( {{\omega _2}} \right) + {\neg }\square \left( {{\omega _3}} \right)\).     

Electromagnetically induced transparency in Λ-system involving D 2 line of Rb atoms confined in sub-micron columns

The effect of electromagnetically induced transparency (EIT) in a Λ-system formed by rubidium atoms contained in thin (10–60 μm) and extremely thin (0.3–5 μm) cells was studied experimentally. It was found that parameters of the EIT resonance degrade slowly in the case where the frequency of the coupling laser is in resonance with the D ₂ transition of rubidium, which enabled the registration of the EIT resonance in a record thin cell with a thickness of L = 390 nm. The specific features of EIT in extremely thin cells reveal themselves when the coupling laser has a frequency detuning Δ from the atomic transition. In this case, the width of the EIT resonance rapidly increases upon an increase in Δ at fixed L (an opposite effect takes place in centimeter-scale cells). It is shown that the width of the EIT resonance is inversely proportional to L in the case of fixed large detuning Δ. The nearly tenfold broadening of the EIT resonance for large values of detuning Δ is caused by the influence of atomic collisions with cell windows on dephasing rate of coherence. The expressions that allow the estimation of the EIT-resonance width for various values of detuning Δ and small values of thickness L are found.     

Peculiarities of the sub-barrier fusion with the quantum diffusion approach

With the quantum diffusion approach the unexpected behavior of the fusion cross-section, angular momentum, and astrophysical S -factor at sub-barrier energies has been revealed. Out of the region of short-range nuclear interaction and action of friction at the turning point the decrease rate of the cross-section under the barrier becomes smaller. The calculated results for the reactions with spherical nuclei are in a good agreement with the existing experimental data.     

Cyanoethylation of Aromatic Aldehyde Imines Containing a Hydroxy Group in the β- or γ-Position. Synthesis of 3-Cyanoethyl-1,3-oxazacycloalkanes

Acrylonitrile reacts with aromatic aldehyde imines containing a hydroxy group in the β- or γ-position to give 70–85% of the corresponding 2-aryl-3-cyanoethyltetrahydro-1,3-oxazines or 2-aryl-3-cyanoethyl-1,3-oxazolidines, respectively. The results of these reactions are rationalized in terms of ring-chain isomerism of the initial imines.__________Translated from Zhurnal Organicheskoi Khimii, Vol. 41, No. 7, 2005, pp. 1064–1066.Original Russian Text Copyright © 2005 by Kon’kova, Abovyan, Khachatryan, Badasyan, Panosyan, Sargsyan.     

Quantum non-Markovian Langevin equations and transport coefficients

Quantum diffusion equations featuring explicitly time-dependent transport coefficients are derived from generalized non-Markovian Langevin equations. Generalized fluctuation-dissipation relations and analytic expressions for calculating the friction and diffusion coefficients in nuclear processes are obtained. The asymptotic behavior of the transport coefficients and correlation functions for a damped harmonic oscillator that is linearly coupled in momentum to a heat bath is studied. The coupling to a heat bath in momentum is responsible for the appearance of the diffusion coefficient in coordinate. The problem of regression of correlations in quantum dissipative systems is analyzed.