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arXiv:2409.05581 · EPJ Quantum Technology

Ramsey-Bordé atom interferometry with a thermal strontium beam for a compact optical clock

Oliver Fartmann, Martin Jutisz, Amir Mahdian, Vladimir Schkolnik, Ingmari C. Tietje, Conrad Zimmermann, Markus Krutzik

Published Mar 3, 2025• 7 citations

Abstract

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 $<4\times 10^{-14} / \sqrt{\tau / {1~s}}$ < 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.

DOI: 10.1140/epjqt/s40507-025-00332-7

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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\times 10^{-14} / \sqrt{\tau / {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.

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.

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.

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 report on our progress toward the realization of an optical frequency standard referenced to strontium intercombination lines. While first frequency measurement of the weakly allowed 1S 0- 3P 1 transition was done with saturation spectroscopy on a thermal beam, we are preparing the experimental setup for high resolution spectroscopy on ultracold atoms of the doubly forbidden 1S 0- 3P 0 line. Our current setup allows the capture more than 10 7 atoms at 1 μK in 500 ms in two stages of magneto-optical trapping. We also demonstrated the dipole trapping of ultracold strontium isotopes for accurate spectroscopy and collisional measurements. A semiconductor laser source at 698 nm has already been locked to a pre-stabilization cavity obtaining a fast linewidth of less than 1 kHz. Second stage stabilization of the clock laser to ultra-high finesse cavity is in development. Recent measurement of elastic and inelastic cross-sections of the two most abundant 88Sr and 86Sr isotopes are also presented.

We report on our progress toward the realization of a compact optical frequency standard referenced to strontium intercombination lines. Our current setup allows the production of ultracold Sr atoms in hundreds of ms. For high resolution spectroscopy of the 1S0-3P0 doubly forbidden transition we have prepared a 698 nm clock laser stabilized on a high finesse, symmetrically suspended cavity and a high power 813 nm light source for the optical lattice trap at the magic wavelength. Due to their compactness, reliability, and low power consumption, semiconductor laser sources represent the best choice for the development of compact and transportable devices for application both on Earth and in Space. A new Sr trapping and cooling experimental setup is also presented.