Precise frequency measurements of atomic transitions by use of a Rb-stabilized resonator

We demonstrate a technique for frequency measurements of atomic transitions with a precision of 30 kHz. The frequency is measured with a ring-cavity resonator whose length is calibrated against a reference laser locked to the D2 line of 87Rb, the frequency of which is known with 10-kHz accuracy. We have used this method to measure the hyperfine structure in the 5P(3/2) state of 85Rb. We obtain precise values for the hyperfine constants, A = 25.041(6) MHz and B = 26.013(25) MHz, and a value of 77.992(20) MHz for the isotope shift in the D2 line.