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IEEE Transactions on Instrumentation and Measurement

A Multistanding-Wave Field Microwave Cavity for Compact Cold-Atom Ramsey Clocks

Fasong Zheng, Kun Liu, Weiliang Chen, Wenxia Song, Shaoyang Dai, Yani Zuo, Shiying Cao, Fang Fang

Published Jan 1, 2026• 0 citations
Publisher

Abstract

Compact cold-atom frequency standards, characterized by low frequency drift and high accuracy, continue to attract significant interest to address the growing demand for portable, high-performance time-keeping solutions. This paper presents and experimentally demonstrates a proof-of-principle prototype of a compact cold-atom Ramsey clock. The system is based on a multi-standing-wave field microwave cavity operating in the TE₀₁₃ mode and employs a free-falling atom scheme to simplify optical frequency control. The chosen TE₀₁₃ cavity is a cylindrical microwave resonator (CMR) fabricated from oxygen-free copper (OFC), which offers advantages in size and microwave leakage control over the conventional TE₀₁₁ cavity for this free-fall configuration. Its structure, which also serves as the vacuum chamber, is sealed with ceramic windows and coupled via rectangular waveguides. During operation, atoms interact with the first and third standing-wave fields to implement Ramsey interrogation. Experimental results show optimal pulse timing with τ1=16 ms, which aligns closely with theoretical predictions (τ1=16.1 ms). The measured central Ramsey fringe has a full width at half maximum (FWHM) of 8.9 Hz and a contrast of 89.1%, corresponding to a measured relative frequency instability of 6.4×10−13τ-1/2.

DOI
10.1109/tim.2026.3682826

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Compact cold-atom frequency standards, characterized by low frequency drift and high accuracy, continue to attract significant interest to address the growing demand for portable, high-performance time-keeping solutions. This paper presents and experimentally demonstrates a proof-of-principle prototype of a compact cold-atom Ramsey clock. The system is based on a multi-standing-wave field microwave cavity operating in the TE₀₁₃ mode and employs a free-falling atom scheme to simplify optical frequency control. The chosen TE₀₁₃ cavity is a cylindrical microwave resonator (CMR) fabricated from oxygen-free copper (OFC), which offers advantages in size and microwave leakage control over the conventional TE₀₁₁ cavity for this free-fall configuration. Its structure, which also serves as the vacuum chamber, is sealed with ceramic windows and coupled via rectangular waveguides. During operation, atoms interact with the first and third standing-wave fields to implement Ramsey interrogation. Experimental results show optimal pulse timing with τ1=16 ms, which aligns closely with theoretical predictions (τ1=16.1 ms). The measured central Ramsey fringe has a full width at half maximum (FWHM) of 8.9 Hz and a contrast of 89.1%, corresponding to a measured relative frequency instability of 6.4×10−13τ-1/2.
Abstract To improve the Ramsey fringe contrast for a portable free-falling-typed cold-atom microwave clock based on a TE 013 -mode cylindrical microwave resonator, this paper innovatively designs an irregular-shaped Ramsey cavity based on the combination of TE 011 and TE 013 modes cylindrical microwave resonators. To ensure b 1 𝜏 1 = b 2 𝜏 2 during the two Ramsey microwave pulses, this study constructs a 3D electromagnetic model to analyze the relationship between the matching factor η = b 1 𝜏 1 /b 2 𝜏 2 and the cavity structural parameters. Simulation results demonstrate that the irregular-shaped Ramsey cavity can effectively generate four spatially separable microwave standing wave fields, with two of them differing in height. The cavity is designed to achieve a central Ramsey fringe with a full width at half maximum (FWHM) of about 9 Hz. By iteratively refining the cavity geometry, the optimal parameters for the cavity dimensions were obtained, with a TE 013 mode height of 100.56 mm and a TE 011 mode height of 34.09 mm. This configuration achieves an amplitude-transit time matching factor η of unity ( η = 1).
We introduce a compact atomic clock based on laser-cooled atoms trapped inside a loop-gap microwave cavity. The cavity occupies a volume eight times smaller than conventional cylindrical cavities while maintaining a high quality factor in the presence of the ten apertures required for optical manipulation of cold atoms. The measured linewidth of the Ramsey spectrum, which is limited by the free fall distance of the atomic cloud in the cavity, was 19.6 Hz. The corresponding frequency instability was σy(τ) = 2.5 × 10−12 τ−1/2, which could be further improved by reducing the local oscillator noise. This work paves a way toward high-performance portable atomic clocks.
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.
We present a scheme for a compact rubidium cold-atom clock which performs diffuse light cooling, microwave interrogation, and detection of the clock signal in a cylindrical microwave cavity. The diffuse light is produced by laser light reflection at the inner surface of the microwave cavity. The pattern of the injected laser beams is specially designed to accumulate the majority of the cold atoms in the center of the microwave cavity. Microwave interrogation of the cold atoms in the cavity leads to Ramsey fringes, which have a linewidth of 24.524.524.5 Hz with a contrast of 95.695.6%95.6 when the free evolution time is 20 ms. Recently, a frequency stability of $7.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}\phantom{\rule{0.28em}{0ex}}{\ensuremath{\tau}}^{\ensuremath{-}1/2}$ has been achieved. The scheme of this physical package can largely reduce the cold-atom clock complexity and increase clock performance.
We present a compact cold-atom clock configuration where isotropic laser cooling, microwave interrogation, and clock signal detection are successively performed inside a spherical microwave cavity. For ground operation, a typical Ramsey fringe width of 20 Hz has been demonstrated, limited by the atom cloud's free fall in the cavity. The isotropic cooling light's disordered properties provide a large and stable number of cold atoms, leading to a high signal-to-noise ratio limited by atomic shot noise. A relative frequency stability of $2.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}{\ensuremath{\tau}}^{\ensuremath{-}1/2}$ has been achieved, averaged down to $4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}$ after $5\ifmmode\times\else\texttimes\fi{}{10}^{3}$ s of integration. Development of such a high-performance compact clock is of major relevance for on-board applications, such as satellite-positioning systems. As a cesium clock, it opens the door to a new generation of compact primary standards and timekeeping devices.
Additive manufacturing (AM) of passive microwave components is of high interest for the cost-effective and rapid prototyping or manufacture of devices with complex geometries. Here, we present an experimental study on the properties of recently demonstrated microwave resonator cavities manufactured by AM, in view of their applications to high-performance compact atomic clocks. The microwave cavities employ a loop-gap geometry using six electrodes. The critical electrode structures were manufactured monolithically using two different approaches: Stereolithography (SLA) of a polymer followed by metal coating and Selective Laser Melting (SLM) of aluminum. The tested microwave cavities show the desired TE011-like resonant mode at the Rb clock frequency of ≈6.835 GHz, with a microwave magnetic field highly parallel to the quantization axis across the vapor cell. When operated in an atomic clock setup, the measured atomic Rabi oscillations are comparable to those observed for conventionally manufactured cavities and indicate a good uniformity of the field amplitude across the vapor cell. Employing a time-domain Ramsey scheme on one of the SLA cavities, high-contrast (34%) Ramsey fringes are observed for the Rb clock transition, along with a narrow (166 Hz linewidth) central fringe. The measured clock stability of 2.2 × 10−13 τ−1/2 up to the integration time of 30 s is comparable to the current state-of-the-art stabilities of compact vapor-cell clocks based on conventional microwave cavities and thus demonstrates the feasibility of the approach.