A narrow-linewidth Brillouin laser for a two-photon rubidium frequency standard

High precision portable and deployable frequency standards are required for modern navigation and communication technologies. Optical frequency standards are attractive for their improved stability over their microwave counterparts; however, increased complexities have anchored them in the laboratory. Sacrificing sensitivity of the most stable optical clocks has led to the recent development of deployable and portable optical frequency standards, leveraging hot atomic or molecular vapor. The short term limit for a majority of previous reports on two-photon rubidium standards is either the shot-noise or intermodulation limit hindering the one second fractional frequency stability to around $1\times10^{-13}/\sqrtτ$. The answer for the shot-noise limit is to increase optical power and collected fluorescence, while the intermodulation limit solution requires improvements in laser linewidth, stimulated Brillouin scattering (SBS) lasers are known to reduce frequency noise, suppressing noise of the pump laser at high offset frequencies. We investigate an optical frequency standard based on the two-photon transition in $^{87}$Rb probed with a narrow linewidth photonic integrated circuit SBS laser with a quality factor over 130 million and instantaneous linewidth $<$ 10 Hz. The use of a narrow linewidth clock laser coupled with operating at higher optical intensities yields clock instabilities of $2\times10^{-14}$ at one second, currently the best reported short-term stability for a two-photon rubidium optical frequency standard.

💡 Research Summary

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The paper addresses the pressing need for high‑precision, portable, and deployable frequency standards required by modern navigation, communication, and sensing systems. While optical frequency standards offer superior short‑term stability compared to microwave counterparts, their complexity has traditionally confined them to laboratory environments. Recent efforts have focused on simplifying optical clocks by leveraging hot atomic or molecular vapors, yet two‑photon rubidium (Rb) standards have been limited in short‑term performance by either photon shot‑noise or intermodulation (laser frequency) noise, typically yielding a fractional frequency stability of about 1 × 10⁻¹³ / √τ at one second.

The authors propose a dual‑pronged solution: (1) increase the optical intensity to suppress photon shot‑noise, and (2) employ a narrow‑linewidth stimulated Brillouin scattering (SBS) laser to dramatically reduce intermodulation noise. The SBS laser is fabricated on an ultra‑low‑loss silicon‑nitride (Si₃N₄) photonic integrated circuit. The waveguide (40 nm thick, 11 µm wide) exhibits a propagation loss of 0.1 dB/m, and the microring resonator (radius 11.787 mm) provides a loaded quality factor Q ≈ 1.3 × 10⁸ at 1550 nm. The device reaches Brillouin lasing threshold at only 14 mW pump power and delivers a sub‑hertz fundamental linewidth with an instantaneous linewidth measured below 10 Hz. Compared with a conventional external‑cavity diode laser (ECDL), the SBS output shows a >20 dB reduction in high‑offset frequency noise.

To interrogate the 5 S₁/₂ (F = 2) → 5 D₅/₂ (F = 4) two‑photon transition in ⁸⁷Rb, the 1556 nm SBS output is frequency‑doubled in a periodically poled lithium niobate (PPLN) waveguide, generating up to 100 mW at 778.1 nm. This light is delivered to a heated (100 °C) rubidium vapor cell (50 mm length, 10 mm diameter) with a Gaussian beam waist w₀ = 1.05 mm, achieving an optical intensity sufficient to drive the two‑photon excitation efficiently. Fluorescence at 420 nm from the subsequent 6 P₃/₂ → 5 S₁/₂ decay is collected by a large‑area photomultiplier tube (PMT) through a short‑pass filter. The fluorescence signal is demodulated at 101 kHz (imposed by an electro‑optic modulator, EOM) to produce an error signal. A dual‑integrator servo with ≈20 kHz bandwidth, together with an acoustic‑optic modulator (AOM) acting as the frequency actuator, locks the laser to the peak of the fluorescence signal. Residual amplitude modulation (RAM) is actively suppressed by feeding back to the EOM bias, and a separate InGaAs photodiode monitors laser power and RAM for real‑time environmental correction.

The overall clock performance is modeled by summing contributions from intermodulation noise (σ_IM), shot‑noise (σ_SN), RAM, ac‑Stark shift, Rb‑Rb collisional shift, and reference clock noise (σ_ref) as expressed in Eq. (6). Measured parameters include the two‑photon transition linewidth (476 kHz), optical input power (58.4 mW), mixer gain (g = 0.58), and beam waist. Using these values, the authors compute σ_IM and σ_SN and compare them with experimentally observed Allan deviations. The resulting short‑term fractional frequency instability reaches 2 × 10⁻¹⁴ at τ = 1 s, an order‑of‑magnitude improvement over prior two‑photon rubidium standards and the best reported short‑term stability for this class of devices. Long‑term stability is assessed by heterodyne comparison with a cavity‑stabilized laser (fractional frequency noise 3.5 × 10⁻¹⁵ at 1 s, drift 2.5 kHz/day) and a vector‑atomic iodine standard (Evergreen‑30). The cavity‑stabilized laser exhibits excellent short‑term performance, while the iodine reference provides a stable long‑term reference.

Key insights from the work include:

1. SBS lasers on Si₃N₄ platforms effectively suppress high‑offset frequency noise, directly addressing the intermodulation limit that has constrained two‑photon Rb clocks.
2. Operating at higher optical intensities, combined with efficient fluorescence collection (≈7–8 % collection efficiency), reduces photon shot‑noise to a negligible level without incurring prohibitive ac‑Stark shifts.
3. Integrated photonic and electronic control (EOM, AOM, RAM servo, dual‑integrator loop) enables precise mitigation of environmental perturbations such as power fluctuations, RAM, and temperature‑induced shifts.
4. The demonstrated Q‑factor and sub‑10 Hz linewidth are compatible with compact, low‑power implementations, suggesting that the approach can be scaled to field‑deployable optical clocks.

In conclusion, the authors have shown that a photonic‑integrated SBS laser, when combined with a high‑intensity two‑photon rubidium interrogation scheme, can achieve a fractional frequency instability of 2 × 10⁻¹⁴ at one second—surpassing all previously reported results for two‑photon Rb standards. This work paves the way for portable optical frequency references that retain laboratory‑grade short‑term stability while meeting the size, weight, and power constraints of real‑world navigation and communication applications.