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Review of Scientific Instruments

Compact two-photon optical clock with a long-term stability of 8.1 × 10−15 without linear drift removal

Chen Feng, Xinrui Luo, Ji’an Duan, Hangzhe Lyu, Lin-Yan Yu, X. B. Qi, Qi-Fan Yang, Yanhui Wang

Published Dec 1, 2025• 3 citations
Publisher

Abstract

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.

DOI
10.1063/5.0291881

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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.
We demonstrated a compact 780 nm rubidium optical clock, which includes an optical frequency standard and an optical frequency comb, with an optical volume of 11.6 liters. Unlike the 778 nm rubidium atomic clocks based on two-photon transition, here, the laser frequency is stabilized to the Rb D2 transition, using modulation transfer spectroscopy. This approach effectively eliminates Doppler background and provides a high signal to noise ratio and high sensitivity. A nearly 300 MHz microwave signal, whose phase exactly tracks that of the optical frequency standard, is generated via the optical frequency comb, yielding a frequency instability of 1.91 E-13 @1 s and 5.29 E-14 @1000 s in the electronic domain. To the best of our knowledge, this is the most precise frequency stabilization result for the first-excited-state transition of alkali metal atoms to date and represents the first optical clock based on this transition. These results offer a promising approach for the development of portable optical clocks.
Rubidium two-photon frequency standards are emerging as powerful contenders for compact, durable devices with exceptional stability. To date, the field has focused on single-color excitation; here, we demonstrate the key advantages of a two-color excitation of a two-photon optical frequency standard based on the $5{S}_{1/2}\ensuremath{\rightarrow}5{D}_{5/2}$ transition of rubidium-87 using driving fields at 780 and 776 nm. Using the 5P3/25{P}_{3/2}5P3/2​ intermediate state to resonantly enhance the transition, we show that frequency stabilities comparable to rubidium single-color two-photon frequency standards can be attained, notably with approximately tenfold lower optical power and tenfold lower rubidium vapor density. Optimization of the detuning from the 5P3/25{P}_{3/2}5P3/2​ intermediate state and of the optical powers of the driving lasers has a dramatic effect on the frequency stability, achieving the best short-term stability of any two-photon rubidium frequency standard to date: $6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$ at $\ensuremath{\tau}=1$ s. We demonstrate that this level of performance is compatible with a compact geometry by fully self-referencing the frequency standard using an integrated fiber frequency comb to simultaneously stabilize the 780-nm laser's detuning from the 5P3/25{P}_{3/2}5P3/2​ intermediate state, producing a frequency-stable microwave output. A comprehensive noise characterization underpins our observations of this two-color frequency standard, explaining the measured stability and showing that this frequency standard is initially shot-noise limited before becoming limited by light shifts in the long term. This work represents a major advance toward a low size, weight, and power frequency standard based on two-color excitation.
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.
A compact rubidium optical clock is presented, incorporating an optical frequency standard, a fiber frequency comb, and associated control electronics. Modulation transfer spectroscopy, devoid of Doppler background and characterized by a high signal-to-noise ratio and sensitivity, is employed to lock the laser frequency to the hyperfine transitions of rubidium atomic lines. The clock exhibits a short-term stability of 4.10 × 10-13at a 1-second gate time, and the stability remains below 7.27 × 10-13up to 1000 seconds. These results offer a promising alternative approach for the development of portable optical clocks.