Line shape analysis for precision spectroscopy in Ba+ ions

Abstract

Most precise tests of the Standard Model (SM) in particle physics set stringent bounds on New Physics models and enable searches for new Physics beyond the SM. Conducting precision experiments on Atomic Parity Violation (APV) paves a way to determine the SM parameter Weinberg angle (sin 2 θ W ) at low energies. Knowledge of atomic wave functions arbitrates the precision to which sin 2 θ W can be determined. Calculations on atomic systems with a single valence electron such as Ba + and Ra + are possible with sufficient accuracy for this purpose. Such an experiment becomes feasible, if a single ion is localized to better than one optical wavelength in order to have the ion in the maximum of the electric and the magnetic fields of two standing waves which drive the two relevant transitions.Measurements on a single trapped 138 Ba + ion for the detailed understanding of atomic structure at percent level precision have been performed with laser spectroscopy referenced to an optical frequency comb. The one-photon and two-photon components of the line shape are extracted using an eight-level optical Bloch model. Measurement of transition frequencies in different Ba + isotopes, 136 Ba + and 134 Ba + enable the determination of isotope shifts. An analysis employing Fano line profiles provides for extracting the transition frequencies between the lowest lying S, P and D states in Ba + isotopes within 200 kHz. Furthermore, systematic effects are investigated by comparing multiple measurement schemes on trapped Ba + ions in a radio frequency Paul-trap setup.Transitions in molecular 127 I 2 serve as reliable secondary frequency standards. The line shape of signals from frequency modulated saturated absorption spectroscopy of hyperfine transitions in 127 I 2 is analyzed. The derived line shape includes effects arising from experimental parameters. Consistent results for line center, density broadening and density shift of spectral lines to 10 −11 relative accuracy have been obtained.Precise spectroscopy is a major prerequisite for an experiment to determine atomic parity violation. This work is an important step towards a precise determination of sin 2 θ W with some 5 fold improvement over the previous best measurement in one week of actual measurement time.We summarize here the main contents of the paper where it distinguishes itself from the treatment in Chapter 5 of this thesis. The main contents of this chapter is also published under E. A. Dijck et al. [81], where also additional material is provided. vii Contents 5.4. Determination of transition frequencies in Ba + ion . . . . . 99 5.4.1. Fano model and experimental observation . . . . . . 100

Spectroscopy of Trapped ¹³⁸Ba⁺ Ions for Atomic Parity Violation and Optical Clocks

“…We have done optical spectroscopy of 138 Ba + for an improved determination of the 6s 2 S 1/2 -6p 2 P 1/2 and 5d 2 D 3/2 -6p 2 P 1/2 transition frequencies (Chapter 4). This yielded the most accurate values for the Ba + clock frequencies (at time of publishing) and laid the groundwork for measurements of 134 Ba + and 136 Ba + isotope shifts in our group [156]. For analyzing the optical spectra, we employed a lineshape model based on the optical Bloch equations, extending an existing code [112] to support arbitrary propagation directions and polarization states of the laser light fields.…”

“…We hebben de 6s 2 S 1/2 -5d 2 D 3/2 en 5d 2 D 3/2 -6p 2 P 1/2 overgangsfrequenties bepaald op 146 114 384.0(0.1) MHz en 461 311 878.5(0.1) MHz, respectievelijk [113]. Dit leverde ook de meest nauwkeurigste waarden voor de klok-frequenties van Ba + op (op het moment van publiceren) en legde de basis voor latere metingen van isotoopverschuivingen in 134 Ba + en 136 Ba + in onze groep [156]. Voor het analyseren van de optische spectra gebruikten we een lijnprofielmodel gebaseerd op de optische Bloch-vergelijkingen met acht toestanden, waarbij we een bestaande computercode [112] hebben uitgebreid met ondersteuning voor willekeurige propagatierichtingen en polarisatietoestanden van de laserlichtvelden.…”