Fig. 1. ⁸⁷Rb two-photon transition energy level

Fig. 2. ⁸⁷Rb two-photon optical frequency reference schematic. (a) Optical path and laser locking system; (b) structure of the optical bench; (c) structure of the physical system

Fig. 3. ⁸⁷Rb 5S_1/2(F=2)-5D_5/2(F'=4,3,2,1),420 nm two-photon fluorescence spectrum and related error signal

Fig. 4. Relation of the 5S_1/2(F=2)-5D_5/2 (F'=4) peak of two-photon fluorescence spectrum and optical power

Fig. 5. Effect of temperature of ⁸⁷Rb cell on fluorescence signal

Fig. 6. Frequency shift due to optical power (The dots and solid line indicate the beat frequency data and fitted shift, respectively)

Fig. 7. Frequency distribution obtained by the beat frequency experiment ( the physical system with (A) or without (B) adjustable components for the beat frequency, respectively)

Fig. 8. Schematic diagram of the physical system beam focus (The lower figures show the alignment near the focal point with the reflected light undeflected (left) and deflected by 0.005° (right))

Fig. 9. Effect of modulation width on frequency shift

Fig. 10. Allan variance of our system in the 2.5 h beat frequency experiment