Measurement of magic wavelengths for the 40Ca+ clock transition

We demonstrate experimentally the existence of magic wavelengths and determine the ratio of the oscillator strengths for a single trapped ion. For the first time, two magic wavelengths for the 40Ca+ clock-transition are measured simultaneously with high precision, giving Lamda|mj|=1/2 = 395.7992(7) nm and Lamda|mj|=3/2 = 395.7990(7) nm. By tuning a laser to an intermediate wavelength between two transitions (4s1/2-4p1/2 and 4s1/2-4p3/2) of 40Ca+, the sensitivity of the clock transition Stark shift to the oscillator strengths for the resonance transition has been greatly enhanced. With the measured magic wavelengths, we determine the ratio of the oscillator strengths to sub-0.5% accuracy. Our experimental method may be applied to measure magic wavelengths for other ion clock-transitions, and, promisingly, the measurement of these magic wavelengths paves the way to building lattice ion clocks.