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Light shift mitigation for the 5S-5D two-photon transition in rubidium

Roman Blum, Stefan Kundermann, Thibaud Ruelle, Steve Lecomte, Sylvain Karlen

Published Apr 5, 2024• 0 citations
Publisher

Abstract

The rubidium two-photon optical atomic clock is a promising technology for applications that require a compact yet stable timekeeping device. However, its long-term frequency stability is often limited by the light shift (or AC Stark effect). In a rubidium two-photon frequency standard, we demonstrate in experiment that the light shift of the 778.1 nm wavelength probe beam can be mitigated with another, 1556.2 nm wavelength beam.

DOI
10.1117/12.3027257

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•Jan 1, 2026•0 citations
The rubidium two-photon optical atomic clock is a promising technology for applications that require a compact yet stable timekeeping device. However, its long-term frequency stability is often limited by the light shift (or AC Stark effect). In a rubidium two-photon frequency standard, we demonstrate in experiment that the light shift of the 778.1 nm wavelength probe beam can be mitigated with another, 1556.2 nm wavelength beam.
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.
Two-photon vapor cell-based optical clocks are strong candidates for next-generation portable atomic standards, offering simplicity, compactness, and high performance. Their narrow clock transitions with counter-propagating beams enable first-order Doppler-free operation. However, systematic perturbations such as the AC Stark shift, temperature-induced shift, and drifts resulting from the laser system pose challenges cause instabilities to medium- to long-term performance. This paper provides a comprehensive overview of Rb two-photon vapor cell optical standards, focusing on the long-term performance-limiting effects and potential mitigation strategies, aiming for clock stabilities better than 1 × 10−15 over the averaging time of a day and beyond.
The $5{S}_{1/2}\ensuremath{\rightarrow}5{D}_{5/2}$ two-photon transition in Rb is of interest for the development of a compact optical atomic clock. Here we present a rigorous calculation of the 778.1-nm ac Stark shift $[2.30(4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}{(\mathrm{mW}/{\mathrm{mm}}^{2})}^{\ensuremath{-}1}]$ that is in good agreement with our measured value of $2.5(2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}{(\mathrm{mW}/{\mathrm{mm}}^{2})}^{\ensuremath{-}1}$. We include a calculation of the temperature-dependent blackbody radiation (BBR) shift, and we predict that the clock could be operated either with zero net BBR shift [T=495.9(27)[T=495.9(27)[T=495.9(27) K] or with zero first-order sensitivity [T=368.1(14)[T=368.1(14)[T=368.1(14) K]. Also described is the calculation of the dc Stark shift of $5.5(1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}/(\mathrm{V}/{\mathrm{cm}}^{2}$) as well as clock sensitivities to optical alignment variations in both a cat's eye and a flat mirror retroreflector. Finally, we characterize these Stark effects, discussing mitigation techniques necessary to reduce final clock instabilities.
In this work, we stabilize a 1556.2 nm fiber laser to the 5S1/2 → 5D5/2 two-photon transition in 87Rb in a carefully designed compact physics package. A commercial fiber frequency comb divides the optical frequency into 200 MHz microwave output, which demonstrates a fractional frequency stability of 2.2 × 10-13 at τ = 1 s and 8.1 × 10-15 at τ = 4000 s, without linear drift removal. We analyze the systematic effect on the short-term and long-term stabilities in detail. The short-term and long-term stabilities are limited by shot noise and ac Stark shift, respectively. The rubidium two-photon optical clock is a promising candidate for the next-generation space-borne atomic clock.
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.