87Rb Two-photon Light Shift suppression through control of the excited state Zeeman Shifts

AC Stark effect, also known as light shift effect, is a dominating factor limiting the long-term stability of the rubidium optical clock. We propose a method of locking the laser loop which allows the Zeeman shift to act as a counterbalance to the light shift. In pursuit of this goal, we show detailed calculations for the excited state Zeeman splitting in the intermediate magnetic field regime (0~G to 12~G) and demonstrate measurements with quantitative spectroscopic data confirming to within $\pm$ 90~kHz/G the predicted Zeeman shift calculations for the $F_e = 4, m_f = -2$ transition. In this proof-of-concept setup the method of light shift compensation via Zeeman shift control to within 3.5~kHz is demonstrated. Further improvements in the magnetic field control could enhance the accuracy for controlling the light shift effect to well below 1~kHz, limited by noise in the applied Zeeman shift which is proportional to both the stability of the current in the coil and the Zeeman sensitivity of the chosen transition.