Modeling of atomic systems for atomic clocks and quantum information

This dissertation reports the modeling of atomic systems for atomic clocks and quantum information. This work is motivated by the prospects of optical frequency standards with trapped ions and the quantum computation proposals with neutral atoms in optical lattices.;Extensive calculations of the electric-dipole matrix elements in monovalent atoms are conducted using the relativistic all-order method. This approach is a linearized version of the coupled-cluster method, which sums infinite sets of many-body perturbation theory terms. All allowed transitions between the lowest ns, np1/2, np 3/2 states and a large number of excited states of alkali-metal atoms are evaluated using the all-order method. For Ca+ ion, additional allowed transitions between nd5/2, np 3/2, nf5/2, nf 7/2 states and a large number of excited states are evaluated. We combine D1 lines measurements by Miller et al. [18] with our all-order calculations to determine the values of the electric-dipole matrix elements for the 4pj - 3d j' transitions in K and for the 5pj - 4dj' transitions in Rb to high precision.;The resulting electric-dipole matrix elements are used for the high-precision calculation of frequency-dependent polarizabilities of ground state of alkali atoms. Our values of static polarizabilities are found to be in excellent agreement with available experiments. Calculations were done for the wavelength in the range 300--1600 nm, with particular attention to wavelengths of common infrared lasers. We parameterize our results so that they can be extended accurately to arbitrary wavelengths above 800 nm. Our data can be used to predict the oscillation frequencies of optically-trapped atoms, and particularly the ratios of frequencies of different species held in the same trap. We identify wavelengths at which two different alkali atoms have the same oscillation frequency.;We present results of all-order calculations of static and frequency-dependent polarizabilities of excited np1/2 and np3/2 state in Na, K, Rb, and Cs atoms and evaluate the uncertainties of these values. Both scalar and tensor part of the p state polarizability were calculated. This made the calculations complicated owing to the contributions from p--d transitions. The static polarizability values are found to be in excellent agreement with previous experimental and theoretical results. We used our calculations to identify the "magic" wavelengths at which the ac polarizabilities of the alkali-metal atoms in the ground state are equal to the ac polarizabilities in the excited npj states facilitating state-insensitive cooling and trapping. We list the results for the np 1/2 and np3/2 states separately. Depending on the mj sub levels, the total polarizability of the np3/2 state was calculated either as the sum or as the difference of scalar and tensor contributions. We pointed out the complications involved in the magic wavelength calculations for the mj = +/-3/2 sub levels. We also study the magic wavelengths for transitions between particular np3/2 F'M' and nsFM hyperfine sub levels.;We have proposed a scheme for state-insensitive trapping of neutral atoms by using two-color light at convenient wavelengths. In this scheme, we predict the values of trap and control wavelengths for which the 5s and 5p3/2 levels in Rb atom have same ac Stark shifts in the presence of two laser fields. We also list the trap and control wavelength combinations where one of the laser wavelengths is double the other. The results were listed at same and different trap and control laser intensities. This scheme allows to select convenient and easily available laser wavelength for experiments where it is essential to precisely localize and control neutral atoms with minimum decoherence.;Motivated by the prospect of an optical frequency standard based on 43Ca+, we calculate the blackbody radiation (BBR) shift of the 4s1/2-3d5/2 clock transition of an optical frequency standard based on 43Ca+. We describe the study of the Rydberg-Rydberg interactions for quantum gates with neutral atoms and decoherence mechanisms in the Rydberg gate scheme. We have also studied the properties and decoherence processes of the Rydberg states as they are needed for the understanding of possible achievable gate fidelity. (Abstract shortened by UMI.)...