🔬 atomic physics

A low-volume cold-atom microwave clock with an additively manufactured cavity

This paper presents a compact, low-volume microwave clock using laser-cooled $^{87}$ Rb atoms and an additively manufactured cavity, achieving a signal-to-noise ratio of 370 and a mid-term instability of $6.7\times10^{-14}$ at 30,000 seconds through the implementation of a low-cost mu-metal foil to mitigate quadratic Zeeman shifts.

Original authors: Samuel A. Smith, Sean Dyer, Alan Bregazzi, Rajnandan Choudhury Das, Oliver S. Burrow, Christoph Affolderbach, Gaetano Mileti, Erling Riis, Paul F. Griffin

Published 2026-10-27

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CC BY 4.0

Original authors: Samuel A. Smith, Sean Dyer, Alan Bregazzi, Rajnandan Choudhury Das, Oliver S. Burrow, Christoph Affolderbach, Gaetano Mileti, Erling Riis, Paul F. Griffin

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Timekeeping is the invisible architecture of modern life. It synchronizes the global internet, guides ships across oceans, and keeps power grids humming in unison. For decades, the most precise clocks have been large, delicate machines housed in laboratories, relying on the steady vibration of atoms to mark the passage of a second. Scientists have long sought to shrink these devices, creating portable versions that can travel to remote locations or fit inside vehicles, without sacrificing their incredible accuracy. The challenge lies in the physics: to keep time perfectly, atoms must be cooled to temperatures near absolute zero and held still long enough to be measured, all while being shielded from the slightest magnetic interference. Achieving this in a small, rugged package requires a complete reimagining of how these atomic clocks are built and how they interact with their environment.

A team of researchers has now demonstrated a significant step forward in this effort by building a compact atomic clock that is both smaller and more stable than previous portable versions. The device relies on a cloud of rubidium atoms, which are laser-cooled until they are nearly motionless. In a traditional setup, this process requires a complex array of mirrors and lenses to guide the cooling lasers from every angle. This new design replaces that complexity with a single, flat chip etched with microscopic grooves. When a single beam of light hits this chip, the grooves split and redirect the light to trap the atoms, creating a "magneto-optical trap" with far fewer optical components. This simplification is crucial for making the clock small enough to be deployed in the field.

To measure the time kept by these trapped atoms, the researchers needed a way to ask the atoms a question using microwaves and listen for the answer. They constructed a specialized chamber, shaped like a small box, to house the atoms during this measurement. Instead of machining this chamber from a solid block of metal, which is expensive and difficult to shape for such precise internal dimensions, they used a 3D printer to create it layer by layer. This "additively manufactured" cavity is roughly the size of a small matchbox, yet it creates a perfect environment for the microwave signals to interact with the atoms. The atoms are prepared in a specific state, allowed to fall freely for a fraction of a second while being probed by microwaves, and then measured to see how their internal "ticking" has changed.

The performance of this new clock was impressive. The researchers measured how clearly they could distinguish the signal of the atoms from the background noise, finding a signal-to-noise ratio of 370. This high clarity translates to a short-term stability that is competitive with much larger systems. However, the clock's long-term accuracy faced a hidden obstacle. The Earth's magnetic field, and even tiny fluctuations in the local environment, can nudge the atoms and cause them to drift from their true frequency. In earlier versions of this clock, this magnetic interference limited how well the device could hold its time over periods longer than ten seconds. To solve this, the team wrapped the vacuum chamber containing the atoms in a thin, flexible sheet of special metal designed to block magnetic fields. This low-cost shield was highly effective, reducing the magnetic noise that disturbed the atoms by more than ten times.

With the magnetic interference suppressed, the researchers could observe the clock's true limitations. They found that the next major hurdle was not the atoms themselves, but the temperature of the microwave cavity. As the metal box holding the atoms warmed up or cooled down, even by a tiny amount, the frequency of the clock shifted. By monitoring the temperature and the clock's output simultaneously, they confirmed that these thermal changes were the primary cause of instability in the medium term. When they selected the most thermally stable periods from their data, the clock achieved a remarkable level of precision, drifting by only a tiny fraction over many hours of operation.

This work proves that a high-performance atomic clock can be built using a simplified, scalable design. By combining a micro-fabricated chip for trapping atoms with a 3D-printed microwave cavity and a simple magnetic shield, the researchers have created a device that is compact, easier to manufacture, and highly stable. While the current version still requires improvements in temperature control to reach its full potential, the results show a clear path toward a new generation of portable timekeepers. These devices could soon provide precise timing for navigation systems in areas where satellite signals are unavailable, or for synchronizing communication networks in remote locations, bringing laboratory-grade accuracy to the real world.

Technical Summary: A Low-Volume Cold-Atom Microwave Clock with an Additively Manufactured Cavity

Problem Statement
The development of atomic clocks faces a persistent challenge: reducing the size, weight, and power (SWaP) requirements without compromising timing performance. While microwave atomic clocks based on thermal vapour systems (using pulsed optical pumping) offer excellent short- and medium-term stability, they suffer from buffer-gas-induced shifts and atomic motion limitations. Conversely, cold-atom clocks offer superior long-term holdover and frequency accuracy due to reduced atomic motion and the absence of buffer gases, but they traditionally require complex optical setups and bulky vacuum systems. The specific challenge addressed in this work is the integration of a compact, scalable manufacturing approach with a high-performance cold-atom architecture to create a deployable microwave clock that maintains performance comparable to state-of-the-art systems.

Methodology
The authors present a compact microwave-interrogated atomic clock based on laser-cooled $^{87}\text{Rb}$ atoms. The system employs a double-resonance architecture where optical transitions handle trapping, cooling, state preparation, and detection, while the ground state is interrogated via Ramsey spectroscopy during free-fall.

Trapping and Cooling: The system utilizes a micro-fabricated grating magneto-optical trap (gMOT) located at the base of the vacuum chamber. A single collimated cooling beam (20 mm radius) is incident on the grating chip, reducing optical components and alignment degrees of freedom compared to conventional six-beam MOTs. Atoms are loaded from background vapour (resistively heated dispensers) for 500 ms, followed by an 8 ms polarization-gradient cooling (PGC) phase to reach sub-Doppler temperatures (<20 µK).
Microwave Interrogation: A key innovation is the use of an additively manufactured (3D-printed) loop-gap resonator (LGR) cavity with a volume of approximately 67 cm³. This cavity supports a TE $_{011}$ -like mode with a field orientation factor of $\xi = 97\%$ and a quality factor ( $Q_c$ ) of 360. Ramsey interrogation is performed using two $\pi/2$ pulses separated by a free-evolution time ( $T_R$ ).
Detection: Due to the compact cavity geometry limiting optical access, the system employs absorption detection rather than fluorescence imaging. A linearly polarized probe beam resonant with the $|F=2\rangle \to |F'=3\rangle$ transition measures the population. A three-pulse sequence (probe, repump, probe) normalizes the signal to the total atom number, mitigating shot-to-shot fluctuations.
Magnetic Shielding: To address medium-term instability caused by the quadratic Zeeman shift, the vacuum chamber was enclosed in a low-cost, single-layer mu-metal foil (Aaronia MagnoShield Flex). This reduced the required quantization field from 134 mG to ~20 mG while maintaining fringe contrast.

Key Contributions

Additively Manufactured Cavity: The demonstration of a 3D-printed microwave cavity integrated into a cold-atom clock, significantly reducing the volume and simplifying manufacturing compared to traditional machined cavities.
Compact Architecture: The successful integration of a gMOT and the compact cavity to create a simplified optical and mechanical layout, reducing alignment complexity.
Magnetic Shielding Implementation: The application of a flexible, low-cost magnetic shield that effectively mitigates quadratic Zeeman shifts, allowing for lower bias fields and improved stability.
Performance Characterization: A comprehensive analysis of the clock's stability limits, identifying signal-to-noise ratio (SNR) constraints, cavity pulling effects, and thermal sensitivity.

Results

Short-Term Stability: The system achieved a signal-to-noise ratio (SNR) of 370 at a 1 Hz bandwidth. This corresponds to a short-term stability of $4.7 \times 10^{-12}/\sqrt{\tau}$ . The authors note that the detection system is capable of an SNR up to 1100, but the observed reduction in Ramsey interrogation is attributed to local-oscillator noise converted into population noise.
Medium-Term Stability:
- Without Shielding: The first-generation design was limited by ambient magnetic field fluctuations, resulting in a medium-term stability of $\approx 2 \times 10^{-12}$ .
- With Shielding: The implementation of the mu-metal foil reduced the inferred medium-term fractional frequency instability limit to approximately $1.5 \times 10^{-13}$ at $\tau = 100$ s.
- Thermal Limitations: The dominant limitation in the mid-term was identified as cavity temperature fluctuations (cavity pulling). The measured fractional-frequency temperature sensitivity was $1.47 \times 10^{-12} \text{ K}^{-1}$ , which is higher than the theoretical estimate of $4 \times 10^{-13} \text{ K}^{-1}$ .
Long-Term Stability: By selecting the most thermally stable section of a 48-hour measurement run, the system demonstrated a fractional frequency instability of $1.2 \times 10^{-13}$ at $\tau = 10^4$ s. Using the Théo1 deviation for improved statistical confidence at longer averaging times, the authors measured a stability of $6.7 \times 10^{-14}$ at $\tau = 3 \times 10^4$ s.

Significance and Claims
The paper claims that this work demonstrates a viable pathway toward a compact, scalable, and deployable cold-atom microwave clock. The authors assert that the combination of a gMOT and an additively manufactured cavity successfully reduces optical complexity and manufacturing requirements while maintaining performance comparable to existing systems.

The study highlights that while magnetic shielding has successfully removed the quadratic Zeeman shift as a dominant medium-term limitation, thermal management of the cavity is now the primary bottleneck. The authors conclude that future iterations focusing on improved thermal isolation, active temperature control, and potentially launching the atoms (to extend Ramsey times) or utilizing a 2D MOT for faster loading (to mitigate the Dick effect) will further enhance the clock's performance. The work positions this architecture as a strong candidate for precision timing applications in telecommunications, grid synchronization, and navigation, particularly in GNSS-denied environments.

Technical Summary: A Low-Volume Cold-Atom Microwave Clock with an Additively Manufactured Cavity

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