Testing Fundamental Symmetries on the Atomic Scale

Atomic and molecular systems and the technological possibilities that have emerged enable highest precision measurements of the properties of these systems. In particular, the known fundamental interactions can be thoroughly studied and effects arising from new, yet unknown interactions can be searched for. Violation of the Parity (P) symmetry can be observed in atoms and molecules and it arises from the weak interactions known in the Standard Model of Particle Physics. A possible permanent electric dipole moment (EDM) violates Time Reversal (T) symmetry and would at presently achievable experimental precision indicate new, yet unobserved interaction. Among the presently pursued lines of research are precision measurements of weak interactions in atoms, such as the determination of the weak mixing (Weinberg) angle (sin² theta_W) at low momentum transfer or searches for permanent electric dipole moments on fundamental particles. We will discuss measuring sin² theta_W in ions of heavy alkali earth atoms using single trapped ions such as Ba⁺ and Ra⁺. Such projects require next to precise atomic spectroscopy also quantum optical treatment of the experiments. Simultaneously improved, precise knowledge of atomic theory and associated experimental verification of the methods employed in state-of-the-art calculations. Searches for permanent EDMs in atoms such as ¹²⁹Xe and molecules such as BaF have potential to challenge the presently best limits established for EDMs on diamagnetic atoms and for electrons. The prospected accuracies are possible due to significant improvements by new and novel experimental methods as well as advances in precise calculations on such systems.