Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Rabi pulling effect in a compact cold-atom clock

Haojie Zhao, Bowen Yang, Yuhan Yan, Xuejie Li, B. X. Yu, Meifeng Ye, Ling Xiao, Jinyin Wan, Jianliao Deng, Hua-Dong Cheng

Published Nov 24, 2025• 0 citations
Publisher

Abstract

We theoretically and experimentally investigate the Rabi pulling effect in an integrating sphere cold-atom clock (ISCAC). Rabi pulling in an ISCAC is caused by magnetic-sublevel transitions between hyperfine states and is related to the amplitude of the microwave pulse, the bias magnetic field, and the density distribution of cold atoms. Theoretical analysis shows the Rabi closed-loop scheme reduces microwave power fluctuation sensitivity by two orders compared to the Ramsey scheme. Experimentally, the Rabi closed-loop scheme achieves a long-term frequency stability of $1.9\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}$ at an averaging time of $200\phantom{\rule{0.16em}{0ex}}000$ s.

DOI
10.1103/kb1q-znvl

Related papers

Reaching a few 10-15 long-term stability of integrating sphere cold atom clock

Yaning Wang Yaning Wang, Yan-Ling Meng, Jinyin Wan Jinyin Wan +6 more

We present the long-term stability of the integrating sphere cold atom clock (ISCAC) and analyze its systematic limitations. The relative frequency instability of 2.6×10−15 is reached for an averaging time of 2×105  s. The second-order Zeeman effect and the cavity pulling effect in ISCAC, which would induce the frequency drift from the clock transition, are analyzed. The analytical and experimental results indicate that the cavity pulling effect is the main contribution to the long-term frequency instability of the ISCAC. Further technical improvements to the microwave cavity are also discussed.

Chinese Optics Letters•Jan 1, 2018•4 citations

Distortion of Rabi oscillations in a compact cold-atom clock

Xinchuan Ouyang, Bowen Yang, Qingqing Hu +4 more

We report on experimental measurements and theoretical calculations of Rabi oscillation distortion during rubidium clock transition in a compact cold-atom clock. The distortion of the Rabi oscillations of the clock transition caused by the magnetically sensitive transitions between magnetic sublevels is related to the duration and amplitude of the microwave pulse, the density distribution of cold atoms, and the biased magnetic field inside the microwave cavity. The theoretical calculations agreed well with the experimental results. The Rabi oscillation measurements are beneficial for determining the optimal parameters of a cold-atom clock and identifying the uniformity of the microwave field inside the cavity. This measurement can be extended to the atomic fountain clock and the vapor-cell atomic clock.

Physical Review A•Apr 26, 2021•4 citations

Improvement in medium long-term frequency stability of the integrating sphere cold atom clock

Peng Liu, Hua-Dong Cheng, Yanling Meng +5 more

The medium long-term frequency stability of the integrating sphere cold atom clock was improved. During the clock operation, Rb87 atoms were cooled and manipulated using cooling light diffusely reflected by the inner surface of a microwave cavity in the clock. This light heated the cavity and caused a frequency drift from the resonant frequency of the cavity. Power fluctuations of the cooling light led to atomic density variations in the cavity’s central area, which increased the clock frequency instability through the cavity pulling effect. We overcame these limitations with appropriate solutions. A frequency stability of 3.5×10−15 was achieved when the integrating time τ increased to 2×104 s.

arXiv:1603.01001•Journal of the Optical Society of America B•Jun 7, 2016•10 citations

A microwave amplitude stabilization method for atomic clocks with Ramsey interrogation

Michele Gozzelino, Salvatore Micalizio, Filippo Levi +2 more

We describe a method to stabilize the amplitude of the interrogating microwave field in compact atomic clocks working in a Ramsey approach. In this technique, we take advantage of the pulsed regime to use the atoms themselves as microwave amplitude discriminators. Specifically, in addition to the dependence on the microwave detuning, the atomic signal after the Ramsey interrogation acquires a dependence on the microwave pulse area (amplitude times duration) that can be exploited to implement an active stabilization of the microwave field amplitude, in a similar way in which the Ramsey clock signal is used to lock the local oscillator frequency to the atomic reference. This stabilization results in a reduced sensitivity of the clock frequency to microwave amplitude fluctuations that are transferred to the atoms through the cavity-pulling effect. The proposed technique is then effective to improve the clock stability and drift on medium and long term. We demonstrate the method for a vapor-cell clock working with a hot sample of atoms but it can be extended to cold-atom compact clocks.

•Feb 9, 2018•0 citations

Optical-plus-microwave pumping in a magnetically insensitive state of cold atoms

Yaning Wang, Yanling Meng, Jinyin Wan +5 more

An optical-plus-microwave pumping method is implemented and optimized to pump cold atoms to a magnetically insensitive state in an integrating sphere. This method consists of several optical and microwave pulses with a proper time sequence. The relative population of cold atoms in the Zeeman sublevel $|F=1,{m}_{F}=0\ensuremath{\rangle}$ is tested by measuring the Rabi oscillations and Ramsey fringes with different numbers of optical and microwave pumping pulses, demonstrating that nearly 83% of the cold atoms can be prepared in the clock state. The number of cold atoms in the target state is up to 2.5 times more than that of the optical pumping alone. Thus, the limitation on the stability of an integrating sphere cold-atom clock from atomic noise is estimated to be from $4.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}{\ensuremath{\tau}}^{\ensuremath{-}1/2}$ to $3.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}{\ensuremath{\tau}}^{\ensuremath{-}1/2}$. This method is also suitable for other precision measurements with cold atoms.

Physical Review A•Feb 26, 2018•14 citations

Development of the integrated integrating sphere cold atom clock*

Mingyuan Yu, Yanling Meng, Meifeng Ye +6 more

We develop an integrated integrating sphere cold atom clock (ISCAC), which mainly consists of physical package, laser system, microwave source, and electronics. This compact system is more stable and reliable than the previous version. The experimental results show that the short term frequency stability of 5.4 × 10 − 13 τ − 1 / 2 and 2.9 × 10−15 at 1-day integrating time are achieved.

Chinese Physics B•Jul 1, 2019•10 citations
We theoretically and experimentally investigate the Rabi pulling effect in an integrating sphere cold-atom clock (ISCAC). Rabi pulling in an ISCAC is caused by magnetic-sublevel transitions between hyperfine states and is related to the amplitude of the microwave pulse, the bias magnetic field, and the density distribution of cold atoms. Theoretical analysis shows the Rabi closed-loop scheme reduces microwave power fluctuation sensitivity by two orders compared to the Ramsey scheme. Experimentally, the Rabi closed-loop scheme achieves a long-term frequency stability of 1.9\ifmmode×\else\texttimes\fi10\ensuremath−151.9\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}1.9\ifmmode×\else\texttimes\fi10\ensuremath−15 at an averaging time of 200000200\phantom{\rule{0.16em}{0ex}}000200000 s.
We present the long-term stability of the integrating sphere cold atom clock (ISCAC) and analyze its systematic limitations. The relative frequency instability of 2.6×10−15 is reached for an averaging time of 2×105  s. The second-order Zeeman effect and the cavity pulling effect in ISCAC, which would induce the frequency drift from the clock transition, are analyzed. The analytical and experimental results indicate that the cavity pulling effect is the main contribution to the long-term frequency instability of the ISCAC. Further technical improvements to the microwave cavity are also discussed.
We report on experimental measurements and theoretical calculations of Rabi oscillation distortion during rubidium clock transition in a compact cold-atom clock. The distortion of the Rabi oscillations of the clock transition caused by the magnetically sensitive transitions between magnetic sublevels is related to the duration and amplitude of the microwave pulse, the density distribution of cold atoms, and the biased magnetic field inside the microwave cavity. The theoretical calculations agreed well with the experimental results. The Rabi oscillation measurements are beneficial for determining the optimal parameters of a cold-atom clock and identifying the uniformity of the microwave field inside the cavity. This measurement can be extended to the atomic fountain clock and the vapor-cell atomic clock.
The medium long-term frequency stability of the integrating sphere cold atom clock was improved. During the clock operation, Rb87 atoms were cooled and manipulated using cooling light diffusely reflected by the inner surface of a microwave cavity in the clock. This light heated the cavity and caused a frequency drift from the resonant frequency of the cavity. Power fluctuations of the cooling light led to atomic density variations in the cavity’s central area, which increased the clock frequency instability through the cavity pulling effect. We overcame these limitations with appropriate solutions. A frequency stability of 3.5×10−15 was achieved when the integrating time τ increased to 2×104 s.
We describe a method to stabilize the amplitude of the interrogating microwave field in compact atomic clocks working in a Ramsey approach. In this technique, we take advantage of the pulsed regime to use the atoms themselves as microwave amplitude discriminators. Specifically, in addition to the dependence on the microwave detuning, the atomic signal after the Ramsey interrogation acquires a dependence on the microwave pulse area (amplitude times duration) that can be exploited to implement an active stabilization of the microwave field amplitude, in a similar way in which the Ramsey clock signal is used to lock the local oscillator frequency to the atomic reference. This stabilization results in a reduced sensitivity of the clock frequency to microwave amplitude fluctuations that are transferred to the atoms through the cavity-pulling effect. The proposed technique is then effective to improve the clock stability and drift on medium and long term. We demonstrate the method for a vapor-cell clock working with a hot sample of atoms but it can be extended to cold-atom compact clocks.
An optical-plus-microwave pumping method is implemented and optimized to pump cold atoms to a magnetically insensitive state in an integrating sphere. This method consists of several optical and microwave pulses with a proper time sequence. The relative population of cold atoms in the Zeeman sublevel $|F=1,{m}_{F}=0\ensuremath{\rangle}$ is tested by measuring the Rabi oscillations and Ramsey fringes with different numbers of optical and microwave pumping pulses, demonstrating that nearly 83% of the cold atoms can be prepared in the clock state. The number of cold atoms in the target state is up to 2.5 times more than that of the optical pumping alone. Thus, the limitation on the stability of an integrating sphere cold-atom clock from atomic noise is estimated to be from $4.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}{\ensuremath{\tau}}^{\ensuremath{-}1/2}$ to $3.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}{\ensuremath{\tau}}^{\ensuremath{-}1/2}$. This method is also suitable for other precision measurements with cold atoms.