The subject of this thesis is the study of coherent interaction of light with matter (atoms) to improve the precision measurements and techniques. Special attention is drawn to get the narrow subnatural electromagnetically induced transmission (EIT), electromagnetically induced absorption (EIA) and nonlinear magneto-optic rotation (NMOR) caused by alkali atoms contained in a vapor cell. Subnatural polarization rotation introduces by a strong circularly polarized light in the absence of any external magnetic field was also studied. A detailed theoretical treatment, given in this dissertation, allows to associate each of the features of the spectra with a special physical mechanism. Many quantum phenomena related to interferences, coherences, optical pumping etc. experiments are studied using home-built diode lasers. This thesis also describes laser cooling and trapping of rubidium atoms using two techniques. Deflection of cold atoms horizontally from MOT using pushing beams are discussed in close consideration for the improvements in the precision measurements. This thesis is organized as follows. In Chapter 1, an introduction to the importance of sub-natural narrow resonance and simplified technique in the precision measurement will be discussed. In Chapter 2, an introduction to EIT, EIA and NMOR resonance are discussed. This chapter will provide a basic theoretical background of atom-field interactions, especially for Λ-type and N -type systems and its steady state solution using density matrix analysis and experimental tools. The most important notion of laser cooling of atoms, ions or molecule i.e., exchange of momentum between light and atoms combining with the Doppler effect will be discussed. In Chapter 3, the observation of subnatural EIT and subnatural EIA in closed and open degenerate two-level system using room temperature vapor cell filled with Rb will be presented. Physical mechanisms that contribute to EIT and EIA, and the contrast of our results from the coherent population trapping (CPT)–type resonances are discussed in detail in appendix A.2 according to our experimental results. In Chapter 4, the narrowing of subnatural EIT and subnatural EIA linewidth in closed and open systems again in degenerate two level transition, using the “Laguerre-Gaussian” control beam instead of generally studied Gaussian beam, will be discussed in detail. In Chapter 5, the conversion between subnatural EIT to subnatural EIA in a degenerate Λ system will be discussed. The physical mechanism created by the introduction of a coherent counter propagating control laser to the co-propagating probe and the control laser are studied. The effect of polarization and axial velocity Doppler averaging will also be studied. In Chapter 6, we will discuss the sensitive technique for precise measurement of small magnetic fields using the NMOR, by chopping the resonant laser beam. We will study the sensitivity and the potential application of this technique in the measurement of an atomic electric-dipole moment. In Chapter 7, we will be studying about the induced optical rotation by a circularly polarized control laser on the linearly polarized probe laser. The effect of the intensity of the control laser beam on the higher order optical rotation will also be studied. In Chapter 8, we will be studying about the cooling and trapping of 87Rb in magneto-optic trap. We will be studying two techniques of trapping of atoms in MOT. The cold cloud of atoms from the MOT are deflected horizontally by using different configuration of pushing beam are studied. A brief summary and outlook of my thesis work will be discussed at Chapter 9.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第21327号 / 理博第4423号 / 新制||理||1635(附属図書館) / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)准教授 COLLINS,Benoit Vincent Pierre, 教授 泉 正己, 教授 日野 正訓 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

This thesis considers new methods that exploit recent developments in computer technology to address three extant problems in the area of Finance and Econometrics. The problem of Asian option pricing has endured for the last two decades in spite of many attempts to find a robust solution across all parameter values. All recently proposed methods are shown to fail when computations are conducted using standard machine precision because as more and more accuracy is forced upon the problem, round-off error begins to propagate. Using recent methods from numerical analysis based on multi-precision arithmetic, we show using the Mathematica platform that all extant methods have efficacy when computations use sufficient arithmetic precision. This creates the proper framework to compare and contrast the methods based on criteria such as computational speed for a given accuracy. Numerical methods based on a deformation of the Bromwich contour in the Geman-Yor Laplace transform are found to perform best provided the normalized strike price is above a given threshold; otherwise methods based on Euler approximation are preferred. The same methods are applied in two other contexts: the simulation of stable distributions and the computation of unit root densities in Econometrics. The stable densities are all nested in a general function called a Fox H function. The same computational difficulties as above apply when using only double-precision arithmetic but are again solved using higher arithmetic precision. We also consider simulating the densities of infinitely divisible distributions associated with hyperbolic functions. Finally, our methods are applied to unit root densities. Focusing on the two fundamental densities, we show our methods perform favorably against the extant methods of Monte Carlo simulation, the Imhof algorithm and some analytical expressions derived principally by Abadir. Using Mathematica, the main two-dimensional Laplace transform in this context is reduced to a one-dimensional problem.