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Physical Review A

Distortion of Rabi oscillations in a compact cold-atom clock

Xinchuan Ouyang, Bowen Yang, Qingqing Hu, Hang-Hang Qi, Ling Xiao, Jinyin Wan, Hua-Dong Cheng

Published Apr 26, 2021• 4 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.103.043118

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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.
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 200000200\phantom{\rule{0.16em}{0ex}}000200000 s.
We report on the experimental measurement of the dc and microwave magnetic field distributions inside a recently developed compact magnetron-type microwave cavity mounted inside the physics package of a high-performance vapor-cell atomic frequency standard. Images of the microwave field distribution with sub-100-μm lateral spatial resolution are obtained by pulsed optical-microwave Rabi measurements, using the Rb atoms inside the cell as field probes and detecting with a CCD camera. Asymmetries observed in the microwave field images can be attributed to the precise practical realization of the cavity and the Rb vapor cell. Similar spatially resolved images of the dc magnetic field distribution are obtained by Ramsey-type measurements. The T2relaxation time in the Rb vapor cell is found to be position dependent and correlates with the gradient of the dc magnetic field. The presented method is highly useful for experimental in situ characterization of dc magnetic fields and resonant microwave structures, for atomic clocks or other atom-based sensors and instrumentation.
We report on a theoretical analysis of the phase-shift in compact atomic clocks working either with cold or thermal atoms. It is well known that in a microwave cavity with electromagnetic losses, a traveling wave adds to the standing wave of a given resonant mode. We calculate the spatial varying phase related to this travelling wave for two geometries of interest in clock applications, the cylindrical cavity and the spherical cavity. Due to their motion, the atoms probe different regions of the cavity and then experience different phases of the interrogating microwave field. We show that this combination of atomic motion and spatial changing phase results in a phase-shift of the clock frequency, well known in primary frequency standards, that can affect the metrological performances also of vapor cell and compact cold-atom clocks. In the latter case, we evaluate the phase-shift for a space clock and a ground clock.
In vapor cell atomic clocks the atom-field interaction is typically obtained inside a microwave cavity resonator in which the microwave driving field together with a static magnetic field and an optical field are applied to excite the atoms. These fields are generally well-controlled, mutually aligned to a common quantization axis. Since the exploited atomic transition is sensitive to any potential axis misalignment, the performance of the clock can also be affected. We study the effect of such misalignment for the case of a cylindrical cavity used in vapor-cell atomic clocks, taking into account the misalignments of the optical detection field and the static magnetic field required for the atomic transition. Both the geometry of the cavity and the factors contributing to losses can play role in the degradation of the signal and are taken into account in the misalignment problem discussed.
The performance of space cold atom clocks (SCACs) should be improved thanks to the microgravity environment in space. The microwave interrogation cavity is a key element in a SCAC. In this paper, we develop a microwave interrogation cavity especially for the rubidium SCAC. The interrogation cavity has two microwave interaction zones with a single feed-in source, which is located at the center of the cavity for symmetric coupling excitation and to ensure that the two interaction zones are in phase. The interrogation cavity has a measured resonance frequency of 6.835056471 GHz with a loaded quality factor of nearly 4200, which shows good agreement with simulation results. We measure the Rabi frequency of the clock transition of the rubidium atom in each microwave interaction zone, and subsequently demonstrate that the distributions of the magnetic field in the two interaction zones are the same and meet all requirements of the rubidium SCAC.
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.