Precision spectroscopy with a single Ca-40(+) ion in a Paul trap

Precision measurement of the 4s(2)S(1/2)-3d(2)D(5/2) clock transition based on Ca-40(+) ion at 729 nm is reported. A single Ca-40(+) ion is trapped and laser-cooled in a ring Paul trap, and the storage time for the ion is more than one month. The linewidth of a 729 nm laser is reduced to about 1 Hz by locking to a super cavity for longer than one month uninterruptedly. The overall systematic uncertainty of the clock transition is evaluated to be better than 6.5 x 10(-16). The absolute frequency of the clock transition is measured at the 10(-15) level by using an optical frequency comb referenced to a hydrogen maser which is calibrated to the SI second through the global positioning system (GPS). The frequency value is 411 042 129 776 393.0(1.6) Hz with the correction of the systematic shifts. In order to carry out the comparison of two Ca-40(+) optical frequency standards, another similar Ca-40(+) optical frequency standard is constructed. Two optical frequency standards exhibit stabilities of 1 x 10(-14) tau(-1/2) with 3 days of averaging. Moreover, two additional precision measurements based on the single trapped Ca-40(+) ion are carried out. One is the 3d(2)D(5/2) state lifetime measurement, and our result of 1174(10) ms agrees well with the results reported in [Phys. Rev. A 62 032503 (2000)] and [Phys. Rev. A 71 032504 (2005)]. The other one is magic wavelengths for the 4s(2)S(1/2)-3d(2)D(5/2) clock transition; lambda(vertical bar mj vertical bar =1/2) = 395.7992(7) nm and lambda(vertical bar mj vertical bar =3/2) = 395.7990 (7) nm are reported, and it is the first time that two magic wavelengths for the Ca-40(+) clock-transition have been reported.