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arXiv:2409.13512 · Physical Review Letters

Cold Beam Optical Clock with Multifrequency Spectroscopy

William G. Tobias, Bryan Hemingway, Steven Peil

Published Jan 27, 2025• 9 citations
arXivHTMLPDF

Abstract

We demonstrate an optical clock based on Ramsey-Bordé interferometry in a laser-cooled ^{40}Ca beam. The mean velocity is reduced by an order of magnitude relative to a thermal beam and the transverse temperature approaches the Doppler limit, enabling the measurement of sub-kHz linewidth fringes in a compact interferometer. Using tailored phase and intensity modulation of the spectroscopy laser to add uniform frequency sidebands, we interrogate atoms throughout the transverse velocity distribution, increasing the Ramsey-Bordé fringe amplitude by a factor of 14 and improving the Allan deviation to 3.4×10^{-15} at one second averaging time.

DOI
10.1103/physrevlett.134.043401

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Conference on Precision Electromagnetic Measurements•Jul 1, 2018•1 citation
We demonstrate an optical clock based on Ramsey-Bordé interferometry in a laser-cooled ^{40}Ca beam. The mean velocity is reduced by an order of magnitude relative to a thermal beam and the transverse temperature approaches the Doppler limit, enabling the measurement of sub-kHz linewidth fringes in a compact interferometer. Using tailored phase and intensity modulation of the spectroscopy laser to add uniform frequency sidebands, we interrogate atoms throughout the transverse velocity distribution, increasing the Ramsey-Bordé fringe amplitude by a factor of 14 and improving the Allan deviation to 3.4×10^{-15} at one second averaging time.
Abstract Compact optical atomic clocks have become increasingly important in field applications and clock networks. Systems based on Ramsey-Bordé interferometry (RBI) with a thermal atomic beam seem promising to fill a technology gap in optical atomic clocks, as they offer higher stability than optical vapour cell clocks while being less complex than cold atomic clocks. Here, we demonstrate RBI with strontium atoms, utilizing the narrow "Equation missing" intercombination line at 689 nm, yielding a 60 kHz broad spectral feature. The obtained Ramsey fringes for varying laser power are analyzed and compared with a numerical model. The "Equation missing" transition at 461 nm is used for fluorescence detection. Analyzing the slope of the RBI signal and the fluorescence detection noise yields an estimated short-term stability of <4×10−14/τ/1 s<4\times 10^{-14} / \sqrt{\tau / {1~s}}<4×10−14/τ/1 s​ < 4 × 10 − 14 / τ / 1 s . We present our experimental setup in detail, including the atomic beam source, frequency-modulation spectroscopy to lock the 461 nm laser, laser power stabilization and the high-finesse cavity pre-stabilization of the 689 nm laser. Our system serves as a ground testbed for future clock systems in mobile and space applications.
This dissertation details the developments of a calcium thermal beam atom interferometer designed to act as an ultra-stable frequency reference over a broad range of timescales. The obtained fractional frequency instabilities of the final apparatus reached ≤ 10−16 after 10's of seconds of averaging without the aid of vibration isolation or significant apparatus temperature stabilization. The vastly superior stability performance of this calcium system compared to other thermal atomic references was facilitated by the enormous atom numbers from the thermal beam, which can be efficiently addressed with Bord\'e-Ramsey spectroscopy on the well-studied (4s2)1S0-(4s4p)3P1 (m=0) clock transition in neutral 40Ca. This method yields interrogation laser frequency dependent interference fringes with a linewidth of 1.6 kHz. This measurement is further enhanced with an electron-shelving detection scheme used for state detection after the interferometry process, causing each excited state atom to emit many hundreds of photons in the detection region. The exceptional instability results from this atom interferometer highlight an underutilized realm of precision measurement science based on relatively simple thermal ensembles. An intuitive understanding of the Bordé-Ramsey process is presented and relevant experimental techniques explained such that this dissertation should prove useful to a broad readership.
We demonstrate Ramsey-Bordé (RB) atom interferometry for high performance laser stabilization with fractional frequency instability <2×10^{-16} for timescales between 10 and 1000s. The RB spectroscopy laser interrogates two counterpropagating ^{40}Ca beams on the ^{1}S_{0}-^{3}P_{1} transition at 657 nm, yielding 1.6 kHz linewidth interference fringes. Fluorescence detection of the excited state population is performed on the (4s4p) ^{3}P_{1}-(4p^{2}) ^{3}P_{0} transition at 431 nm. Minimal thermal shielding and no vibration isolation are used. These stability results surpass performance from other thermal atomic or molecular systems by 1 to 2 orders of magnitude, and further improvements look feasible.
Atomic beam optical clocks offer continuous operation, simplified structure, and excellent short- to mid-term stability, making them promising candidates for next-generation optical flywheel clocks. However, the atomic utilization efficiency in current thermal beam optical clocks remains below 1%, limiting their further performance enhancement. Therefore, maximizing the utilization of atoms within the atomic beam has become a critical problem. In this work, we propose an innovative nanosecond Ramsey spectroscopy for Ca beam optical clocks, which enables the full utilization of atoms with all transverse velocities. The spectral amplitude is enhanced 2300 times compared to conventional Ca beam optical clocks, and the frequency stability can reach the quantum projection noise limit of 1.2×10−17/τ1.2\times 1{0}^{-17}/\sqrt{\tau }1.2×10−17/τ​ in theory, comparable to the best cold-atom optical clocks. This approach paves the way for high-precision, transportable flywheel optical clocks.
Atomic clocks provide a reproducible basis for our understanding of time and frequency. Recent demonstrations of compact optical clocks, employing thermal atomic beams, have achieved short-term fractional frequency instabilities of order ${10}^{\ensuremath{-}16}$, competitive with the best international frequency standards available. However, a serious challenge inherent in compact clocks is the necessarily smaller optical beams, which results in rapid variation in interrogating wave fronts. This can cause inhomogeneous excitation of the thermal beam leading to long-term drifts in the output frequency. Here we develop a model for Ramsey-Bord\'e interferometry using optical fields with curved wave fronts and simulate the 40Ca^{40}\mathrm{Ca}40Ca beam clock experiment described by Olson et al. [Phys. Rev. Lett. 123, 073202 (2019)]. The results of Olson et al. showed surprising and unexplained behavior in the response of the atoms in the interrogation. Our model predicts signals consistent with experimental data and can account for the significant sensitivity to laser geometry that was reported. We find the signal-to-noise ratio is maximized when the laser is uncollimated at the interrogation zones to minimize inhomogeneity and also identify an optimal waist size determined by both laser inhomogeneity and the velocity distribution of the atomic beam. We investigate the shifts and stability of the clock frequency, showing that the Gouy phase is the primary source of frequency variations arising from laser geometry.
We demonstrate laser frequency stabilization at the 10-16fractional frequency level in one second through spectroscopy on a 650 °C calcium atomic beam. The calcium beam is interrogated with a cavity stabilized 657 nm laser arranged in a Ramsey-Borde configuration. A second laser at 431 nm reads off the final atomic state populations while allowing for high signal-to-noise. Limitations of this method are being explored and, and, based on current noise analysis, there is potential to achieve fractional frequency stabilities in the 10-17range or below.