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arXiv:2511.19702 · Physical Review Applied

Active compensation of the ac Stark shift in a two-photon rubidium optical frequency reference using power modulation

Yorick Andeweg, John E. Kitching, Matthew T. Hummon

Published Feb 6, 2026• 1 citation
arXivHTMLPDF

Abstract

We implement a feedback protocol to suppress the ac Stark shift in a two-photon rubidium optical frequency reference, reducing its sensitivity to optical power variations by a factor of 1000. This method alleviates the tradeoff between short-term and long-term stability imposed by the ac Stark shift, enabling us to simultaneously achieve instabilities of 3 × 10 − 14 at 1 s and 2 × 10 − 14 at 10 4 s. We also quantitatively describe, and experimentally explore, a stability limit imposed on clocks using this method by frequency noise on the local oscillator.

DOI
10.1103/25md-vv43

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We implement a feedback protocol to suppress the ac Stark shift in a two-photon rubidium optical frequency reference, reducing its sensitivity to optical power variations by a factor of 1000. This method alleviates the tradeoff between short-term and long-term stability imposed by the ac Stark shift, enabling us to simultaneously achieve instabilities of 3 × 10 − 14 at 1 s and 2 × 10 − 14 at 10 4 s. We also quantitatively describe, and experimentally explore, a stability limit imposed on clocks using this method by frequency noise on the local oscillator.
The two-photon transition in rubidium is an attractive candidate for use in the next generation of field-deployable atomic clocks and frequency references. However, this transition is known to suffer from a large AC Stark shift, through which fluctuations in the intensity of the interrogation laser cause fluctuations of the clock frequency, often limiting long-term stability. We implement an interrogation protocol known as the auto-compensated shift (ACS) in a two-photon rubidium optical frequency reference, reducing its sensitivity to optical intensity fluctuations by a factor of 1000. ACS alleviates the tradeoff between short-term and long-term stability imposed by the light shift and enables us to simultaneously achieve a fractional instability of 3 x 10^-14 at an integration time of 1 s and 2 x 10^-14 at an integration time of 10,000 s. We also examine a stability limit imposed on clocks using ACS by frequency noise on the laser.
The two-photon optical transition in rubidium offers a means to a simple, stable optical frequency reference. Here accuracy is limited by frequency drift due to fluctuations in light intensity, while stability is limited by the signal-to-noise ratio of detection. In its traditional implementation there is a tradeoff between accuracy and stability, set by the technical ability to control light intensity. This study uses a two-color excitation scheme for cancellation of light-induced frequency drifts, and replaces fluorescence with absorption in detection, allowing significant improvement of the standard's stability and accuracy.
Atomic clocks are based on highly stable and well-characterized atomic transitions, mak-ing precise control and understanding of systematic frequency shifts essential for improved timekeeping performance. This thesis presents an experimental study of light-induced Stark shifts in rubidium and their impact on precision laser spectroscopy relevant to atomic frequency standards, as well as the effects of residual amplitude modulation on the laser lock point and the resulting sensitivity of both short- and long-term stability. A laser-based spectroscopy system was developed to probe rubidium transitions while enabling controlled variation of optical intensity. The optical beam was experimentally characterized through calculations of beam waist and measurements of power to accurately determine the intensity at the interaction region. Frequency shifts arising from the AC Stark effect were measured as a function of optical power, allowing extraction of the differential polarizability between atomic energy levels using a theoretical model relating energy shifts to electric-field intensity. Uncertainty analysis was performed through systematic propagation of experimental errors associated with beam geometry, optical power calibration, and frequency measurements. In addition, residual amplitude modulation generated by electro-optic phase modulation was investigated as a significant source of systematic error in frequency stabilization systems used in atomic clocks. The magnitude and behavior of RAM were experimentally characterized, and its impact on frequency stability was quantified by measuring the sensitivity of the laser lock point to controlled variations in RAM. Potential mitigation strategies were then explored through active pre-compensation of RAM using an amplitude electro-optic modulator in a closed-loop feedback system.
Abstract 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 Fe=4,mf=−2F_e = 4, m_f = -2Fe​=4,mf​=−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.
We propose a scheme for interrogating a warm rubidium vapor using two different clock lasers. Performance wise, this approach is distinctly different from the recently proposed two-color two-photon rubidium clocks as our scheme does not trade off the ac Stark suppression against an increased sensitivity to the cell temperature or pressure. Instead, our approach compensates both the ac Stark shift and the temperature and pressure-induced frequency shifts. The proposed scheme also makes use of the modulation transfer technique, which enables a two orders of magnitude increase in the signal-to-noise ratio compared to traditional clocks that rely on fluorescence measurements.