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We present the theoretical basis of a cavity-enhanced polarimetric scheme for the measurement of parity-nonconserving (PNC) optical rotation. We discuss the possibility of detecting PNC optical rotation in accessible transitions in metastable Xe and Hg, and ground state I. In particular, the physics of the PNC optical rotation is presented, and we explore the lineshape effects on the expected PNC optical rotation signals. Furthermore, we present an analysis of the eigenpolarizations of the cavity-enhanced polarimeter, which is necessary for understanding the measurement procedure and the ability of employing robust background subtraction procedures using two novel signal reversals. Using recent atomic structure theoretical calculations, we present simulations of the PNC optical rotation signals for all proposed transitions, assuming a range of experimentally feasible parameters. Finally, the possibility of performing sensitive measurements of the nuclear-spin-dependent PNC effects is investigated, for the odd-neutron nuclei $^{129}$Xe and $^{199}$Hg, and the odd-proton nucleus $^{127}$I.
We have further developed and extended a method for calculation of atomic properties based on a combination of the configuration interaction and coupled-cluster approach. We have applied this approach to the calculation of different properties of ato
The combination of configuration interaction and many-body perturbation theory methods (CI+MBPT) is extended to non-perturbatively include configurations with electron holes below the designated Fermi level, allowing us to treat systems where holes p
We propose a method for measuring parity violation in neutral atoms. It is an adaptation of a seminal work by Fortson [Phys. Rev. Lett. {bf 70}, 2383 (1993)], proposing a scheme for a single trapped ion. In our version, a large sample of neutral atom
We demonstrate a new method of cavity-enhanced non-destructive detection of atoms for a strontium optical lattice clock. The detection scheme is shown to be linear in atom number up to at least 10,000 atoms, to reject technical noise sources, to achi
Accurate evaluation of the $mathcal{P}$,$mathcal{T}$-odd Faraday effect (rotation of the polarization plane for the light propagating through a medium in presence of an external electric field) is presented. This effect can arise only due to the $mat