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Optical and Quantum Sensing and Precision Metrology II

Compact ultra-cold and thermal atomic clocks with stabilities better than part-per-trillion at one second

Erling Riis, Paul F. Griffin

Published Mar 5, 2026• 0 citations
Publisher

Abstract

In this talk, I will outline two stands of our ongoing atomic clock research at the University of Strathclyde, aimed at achieving short-term stabilities surpassing 1e-12 in portable systems. Firstly, I present a cold-atom microwave clock that integrates a grating-MOT within an additively manufactured microwave cavity, enabling a compact and potentially highly stable portable system. The work examines noise minimisation techniques through direct comparison with a cold-atom coherent population trapping (CPT) clock. I will also discuss progress on two-photon rubidium clocks based on MEMS vapour cells with integrated optics. The results highlight their prospects for resilient PNT applications and scalable deployment.

DOI
10.1117/12.3089690

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In this talk, I will outline two stands of our ongoing atomic clock research at the University of Strathclyde, aimed at achieving short-term stabilities surpassing 1e-12 in portable systems. Firstly, I present a cold-atom microwave clock that integrates a grating-MOT within an additively manufactured microwave cavity, enabling a compact and potentially highly stable portable system. The work examines noise minimisation techniques through direct comparison with a cold-atom coherent population trapping (CPT) clock. I will also discuss progress on two-photon rubidium clocks based on MEMS vapour cells with integrated optics. The results highlight their prospects for resilient PNT applications and scalable deployment.
The convergence of atomic spectroscopy, MEMS cell technologies and integrated photonics has led to the deployment of high-precision chip-scale atomic devices [1]. In this talk, we will present in-progress studies at FEMTO-ST Institute, France, for the development of microcellbased microwave and optical atomic clocks, with enhanced stability performances. In the first part, we will talk about the demonstration of CPT-based microwave cell clocks with stability at 1 day in the low 10−12 range [2], made possible thanks to the combination of advanced Ramsey-based interrogation sequences [3] and cells built with low gas permeation windows [4-5]. In the second part, we will discuss the in-progress development of a microcell-based optical frequency reference based on the two-photon transition of Rb atom at 778 nm. An encouraging short-term stability of 3 × 10−13 at 1 s and 3 × 10−14 at 100 s has been recently achieved [6]. Future studies will be briefly discussed.
An atomic clock based on a compact source of cold atoms and coherent population trapping (CPT) is an encouraging goal for future low-volume atomic frequency references. Our experiment seeks to investigate the performance of such a system by applying CPT in a high-contrast lin⊥lin polarisation scheme to our 87Rb grating magneto optical trap (GMOT) apparatus. In this paper, we report on our progress of improving short- term stability of our cold-atom CPT apparatus. Our recent measurements have shown a short-term stability of 5 x 10-11/√τ, with the ability to average down for times τ>100s.
Abstract A compact platform for cold atoms opens a range of exciting possibilities for portable, robust and accessible quantum sensors. In this work, we report on the development of a cold-atom microwave clock in a small package. Our work utilises the grating magneto-optical trap and high-contrast coherent population trapping in the lin ⊥ $\perp $ lin polarisation scheme. We optically probe the atomic ground-state splitting of cold 87Rb atoms using a Ramsey-like sequence whilst the atoms are in free-fall. We have measured a short-term fractional frequency stability of 5 × 10 − 11 / τ 5×10−11/τ5{\times}{10}^{-11}/\sqrt{\tau }5×10−11/τ​ with a projected quantum projection noise limit at the 10 − 13 / τ 10−13/τ{10}^{-13}/\sqrt{\tau }10−13/τ​ level.
An optical atomic frequency-reference based on a vapour of atoms is a strong candidate for a creating a portable atomic clock with sufficient stability to be a reliable independent timing system for major infrastructure in the event of GNSS denial. We present the development of optical atomic frequency-standards within the University of Strathclyde, where MEMS vapour cells and lasers have been developed for a miniaturised rubidium frequency-reference. Existing chip-scale systems have been demonstrated by others using a microwave transition, however an optical clock offers a significantly higher frequency to enable a lower instability.
This thesis presents results on two microwave, double-resonance, Rubidium 87 atomic clocks. These studies are motivated by the need for compact and miniature clocks with improved performances or improved Size,Weight and Power (SWaP). A first clock study, covered in chapter 3, focuses on the μPOP clock, the first demonstration of Double Resonance (DR) Ramsey operation in a micro-manufactured hot-vapor cell clock.With a short-termstability of σy(τ ) ≤ 2 × 10−11τ−1/2 and long-termstability of 1.5 × 10−12 at one day, the μPOP clock features state-of-the-art stability for microwave miniature cell clocks. As demonstrated in [1], the μPOP clock short-term stability has been optimized to mitigate the Dick effect and laser Relative Intensity Noise (RIN) contributions, with the latter being the biggest contributor to the short-termstability. The long-terminstability budget shows that the intensity and frequency light shifts contributions are one and two order of magnitudes lower than the measured stability with a contribution of the order of 10−13 and 10−14 at one day, respectively. This confirms the interest of the Pulsed Optically Pumped (POP) approach compared to the ContinuousWave (CW) scheme and sets the potential performances of the μPOP clock. Other long-termcontributors to the instabilities have been evaluated. In the upper limit, the contribution of the cell-temperature shift to the instability is estimated to be two orders of magnitude below the measured stability, confirming the benefit of the N2 and Ar buffer gas-mixture approach for a close to zero cell-temperature sensitivity coefficient. The last two effects, the microwave-power and the position shifts are the greatest contributor to the mid and long-termstability with the latter being the limiting long-term phenomenon whose contribution must be carefully evaluated using the Groslambert covariance. The μPOP studies conclude with the description of a fast and reliable method for measuring the relaxation rates in Ramsey DR vapor-cell clocks. At the nominal cell temperature, namely ≈ 100◦C, the population and coherence relaxations rates are measured to be at the order of 5 kHz and 4 kHz, respectively. Their values have been measured down to 60◦C with both at the order of 1 kHz. Finally, a theoretical model using only parameters taken from the literature has been derived to describe the measured relaxation rates values with agreement within 20%. Chapter 4 focuses on the simulation and realization of a microwave cavity for a DR cold-atom clock using a GratingMagneto-Optical Trap (GMOT). The final cavity shows a low quality factor of Q ≈ 360 which is in the interest of reducing the cavity-pulling shift. The TE011-like cavity mode is separated by at least 500 MHz from the neighbouring modes as predicted by the simulations. The same simulations allowed to effectively predict the cavity’s resonance frequency with a small error of 60 MHz which can easily be compensated by the cavity frequency tuning mechanism. The expected simulated excellent properties of the resonance mode in termof microwave field uniformity and homogeneity are confirmed by measurement of the field field orientation factor of 97% and low Rabi oscillation damping, respectively. Chapter 5 focuses on the integration of the microwave cavity in a clock setup designed by Erling Riis group from the university of Strathclyde. The clock described in this chapter is the first realization of a DR Ramsey Rb cold-atom clock using a GMOT for cooling and trapping which reduces the clock footprint. In practise, ≈ 106 atoms at ≈ 10 μK are loaded thanks to the grating. Ramsey fringes were successfully obtained with Ramsey times up to 20 ms, limited by the clock geometric design. The clock implements state-selection that allows for increased Signal-to-Noise Ratio (SNR) and better short-term stability of ≈ 1.5 × 10−11τ−1/2. This stability is well-explained by SNR of the fringes. Long-term stability is dominated by the 2nd-order Zeeman shift contribution as the clock is not magnetically shielded. The two studies presented in this thesis, namely the μPOP and cold-atom clocks, pave the way towards more miniature and compact frequency standards, respectively. Further improvements of the former would yield a intensity light shift limited clock with ≈ 10−13 stability at one day. Further version of the latter clock using the cavity as standalone vacuum system would allow for reduced SWaP cold-atom frequency standards.
We present a demonstration of a cold-atom optical-microwave double resonance (DR) Ramsey clock utilising an additively manufactured loop-gap-resonator cavity and grating magneto-optical trap (GMOT). The use of additive manufacturing allows for complex cavity structures, more difficult to produce with traditional machining techniques, while the GMOT architecture significantly simplifies the optical system required to trap and cool the atomic sample. In the current demonstration a single laser is used to trap < 3 × 106 87Rb atoms, cool them to below 10 µK, optically pump and read-out state populations of the atoms after microwave interrogation. A Ramsey-type interrogation scheme is employed with an empirically evaluated optimum free evolution time of 10 ms, limited by the loss of signal due to atoms falling out of the read-out beam. We demonstrate a short-term stability of < 2×10−11τ−1/2, in reasonable agreement with the predicted short-term stability based on the signal to noise ratio of the measured Ramsey fringes. Excellent field homogeneity of the cavity microwave field is demonstrated though Rabi oscillations, while almost complete optical pumping and good field orientation is evidenced by Zeeman spectroscopy of the ground-state hyperfine energy levels. This work is a novel approach towards more compact and portable cold-atom microwave clocks with significant potential for further miniaturization of the system.