Transition frequencies between low-lying energy levels in a single trapped 138 Ba + ion have been measured with laser spectroscopy referenced to an optical frequency comb. By extracting the frequencies of one-photon and two-photon components of the line shape using an eight-level optical Bloch model, we achieved 0.1 MHz accuracy for the 5d 2 D 3/2 -6p 2 P 1/2 and 6s 2 S 1/2 -5d 2 D 3/2 transition frequencies, and 0.2 MHz for the 6s 2 S 1/2 -6p 2 P 1/2 transition frequency.Trapped single ions can be exploited to investigate the interaction between light and matter, and to construct optical clocks [1]. For these applications based on high precision spectroscopy a good understanding of the optical line shapes involved is indispensable. We have employed an optical frequency comb [2] to measure transition frequencies in Ba + and a model based on optical Bloch equations to extract atomic parameters from fluorescence spectra. These are essential ingredients for high precision experiments, in particular for atomic parity violation measurements in single Ba + [3,4] and Ra + ions [5,6] in the search for new physics [7]. In this work the frequencies of transitions between three of the lowest fine structure levels in the 138 Ba + ion are addressed. These levels form a Λ-configuration as shown in Fig. 1. The level 6p 2 P 1/2 decays to the levels 6s 2 S 1/2 and 5d 2 D 3/2 with a branching ratio of about 3:1 [8]. We have measured the transition frequencies in a single 138 Ba + ion by driving the transitions 6s 2 S 1/2 -6p 2 P 1/2 and 5d 2 D 3/2 -6p 2 P 1/2 , employing an optical frequency comb as frequency reference. The dynamics of the population of the 2 P 1/2 level can be described by optical Bloch equations [9][10][11]. Coherent coupling between the 2 S 1/2 and 2 D 3/2 levels is observed when the two laser fields are detuned by the same amount from the respective atomic resonances. In this condition a two-photon process causes coherent population trapping, reducing the population of the 2 P 1/2 level [12]. For the measurements reported here a single Ba + ion is confined in a hyperbolic Paul trap (see Fig. 2). The trap is operated at frequency ω rf /2π = 5.44 MHz with a peak-to-peak rf voltage of typically V rf = 600 V. Additional electrodes provide a dc potential to compensate the effect of mechanical imperfections and stray fields, minimizing the micromotion of the ion in the trap. The trap is loaded by photoionization of 138 Ba atoms with laser light at wavelength 413.6 nm. The trap is mounted in a UHV chamber with residual gas pressure below 10 −10 mbar. Doppler cooling and detection of the Ba + ions is achieved with laser light at wavelengths λ 1 and λ 2 (see Fig 1). Laser light to drive the 6s 2 S 1/2 -6p 2 P 1/2 tran- * e.a.dijck@rug.nl † Present address: Department of Physics, Columbia University, New York, NY 10027 FIG. 1. Low-lying energy levels of the Ba+ ion. The wavelengths of the investigated transitions are given. FIG. 2. Schematic diagram of the hyperbolic Paul trap used for trapping Ba+ ions, consisting of ...

The lifetime of the long-lived 5d 2 D 5/2 level in 138 Ba + ions was measured in trapped single ions and small ion crystals using continuous quantum jump spectroscopy. We find τ D 5/2 = 25.6(0.5) s, significantly below previously reported values. We have verified our result by exploiting camera images of the stored ions, which enabled monitoring the cleanliness and sufficiently low temperature of the ion samples, and investigating common systematic effects.

The lifetime of the metastable 5d 2 D 5/2 state has been measured for a single trapped Ba + ion in a Paul trap in Ultra High Vacuum (UHV) in the 10 −10 mbar pressure range. A total of 5046 individual periods when the ion was shelved in this state have been recorded. A preliminary value τ D 5/2 = 26.4(1.7) s is obtained through extrapolation to zero residual gas pressure.

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

The lifetime of the metastable 5d 2 D 5/2 state has been measured for a single trapped Ba + ion in a Paul trap in Ultra High Vacuum (UHV) in the 10 −10 mbar pressure range. A total of 5046 individual periods when the ion was shelved in this state have been recorded. A preliminary value τ D 5/2 = 26.4(1.7) s is obtained through extrapolation to zero residual gas pressure.