We demonstrate experimentally the existence of magic wavelengths and determine the ratio of oscillator strengths for a single trapped ion. For the first time, two magic wavelengths near 396 nm for the ^{40}Ca^{+} clock transition are measured simultaneously with high precision. By tuning the applied laser to an intermediate wavelength between transitions 4s_{1/2}→4p_{1/2} and 4s_{1/2}→4p_{3/2}, the sensitivity of the clock transition Stark shift to the oscillator strengths is greatly enhanced. Furthermore, with the measured magic wavelengths, we determine the ratio of the oscillator strengths with a deviation of less than 0.5%. Our experimental method may be applied to measure magic wavelengths for other ion clock transitions. Promisingly, the measurement of these magic wavelengths paves the way to building all-optical trapped ion clocks.

The 7 Li + ion is one of the most important candidates for verifying QED theory and obtaining the precise value of the fine-structure constant 𝛼. However, direct laser cooling of trapped Li + ions will lead to strong background fluorescence which will influence the spectrum detection. The sympathetic cooling technique is a good choice to solve the problem. In this work, we report sympathetic cooling of 7 Li + ions to few mK using 40 Ca + ions in a linear Paul trap. A mixed ion crystal of 40 Ca + ions and 7 Li + ions are obtained. We also analyze the motion frequency spectra of pure 40 Ca + ions and mixed ions.

In light of the diverse range of reported values for the lifetimes of metastable states of 40Ca+, we have carried out afresh both measurements and theoretical investigation to confirm the lifetime of its 3d 2D5/2 state (T3rf5/2). A high-efficiency quantum state detection method by monitoring the quantum jumps of a laser-cooled single Ca+ ion in a miniature ring Paul trap was employed in the measurement. Also, sophisticated calculations were performed considering higher order nonlinear terms in the relativistic coupled-cluster (RCC) method with all possible single and double excitations, but accounting only for the important triple excitations from both the core and the valence orbitals. Systematic factors affecting measurement, such as collision with background gases, heating effects, the power of the 866-nm laser, and state detection errors were carefully analyzed. Our observational and theoretical values for r}d5/2 are 1174(10) ms and 1172 (3) ms, respectively, which agree well with the experimental results reported by P. A. Barton et at. [Phys. Rev. A 62, 032503 (2000)] and A. Kreuter etal. [Phys. Rev. A 7 1 ,032504 (2005)]. The present theoretical analysis demonstrates that the contributions from the core triples and Breit interaction are notable, as they improve the theoretical results obtained in the previous RCC calculations [B. K. Sahoo, Phys. Rev. A 74, 062504 (2006)].