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A Ti:sapphire laser at 729 nm is frequency stabilized to an ultra-stable ultra-low thermal expansion coefficient (ULE) cavity by means of Pound-Drever-Hall method. An acousto-optic modulator is used as the fast frequency feedback component. 1 Hz linewidth and 2 × 10(-15) frequency stability at 1-100 s are characterized by optical beating with a separated Fabry-Perot cavity stabilized diode laser. Compared to the universal method that the error signal feedback to inject current of a diode laser, this scheme is demonstrated to be simple and also effective for linewidth narrowing. The temperature of zero coefficient of the thermal expansion of the ULE cavity is measured with the help of a femto-second frequency comb. And the performance of the laser is well defined by locking it to the unperturbed clock transition line-center of 4 S1/2-3 D5/2 clock transition of a single laser cooled (40)Ca(+) ion. A Fourier-transform limited resonance of 6 Hz (Δv/v = 1.5 × 10(-14)) is observed. This laser is also used as the local oscillator for the comparison experiment of two (40)Ca(+) ion optical clocks and improves the stability of comparison for an order of magnitude better than the previous results.

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.