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In order to improve the currently limited Signal-to-Noise Ratio (SNR) of the compact optically pumped cesium beam tubes, we proposed a hexapole magnetic focusing method for the cesium beams. The total number of the detected cesium atoms with a hexapole magnetic system were calculated and found to be 9.5 times higher than that without the hexapole magnetic system. This result gives a prediction of 3.1 fold increase in the SNR when only the shot noise is considered, compared with the conventional tubes. In order to be closely integrated with experimental verification, the hexapole magnetic system was engineered and the simulation results of this structure shown that it not only met the magnetic induction requirements of the simulation under multiple channels, but also had effective magnetic shielding.

We proposed a new method of laser frequency stabilization based on laser spectroscopy induced by bichromatic or polychromatic laser. When the frequency difference of the bichromatic or polychromatic laser is close to the excited state hyperfine level interval, the main physical effect in the process is velocity selective resonance (VSR). However, when the frequency difference of the bichromatic or polychromatic laser is close to the ground state hyperfine level interval, the main physical effect in the process is velocity selective optical pumping (VSOP). Besides, we observed similar laser spectroscopy using a dual-frequency Faraday laser, the high amplitude of the error can be used laser frequency stabilization.

We measure the light shift of the rubidium atomic clock under interaction of a 780 nm laser, which has potential application in the laser power stabilization. At the same time, in order to improve the performance of rubidium clock, we demonstrate a Faraday laser of which the cavity mode is locked to the peak of the transition spectrum, thus suppressing the otherwise existed power and frequency noise caused by the cavity mode fluctuations. This Faraday laser is suitable for the optical pumped rubidium atomic clock with the frequency being stably on resonance with the rubidium 780nm transition, and has potential applications on the cesium beam clocks and fountain clocks.

Two feasible schemes are proposed by laser cooling of alkali atoms to realize the narrow-linewidth, continual superradiant lasing. Utilizing the D1 gray molasses to realize a cloud of cold Cs atoms for the two-level Faraday active optical clock (AOC), the effect of Doppler broadening on the transmission bandwidth of Faraday atomic filter will be effectively suppressed to the level of natural linewidth. Thus, the influence of mechanical or thermal vibrations of cavity mirrors on the clock laser will be decreased by about 102 times, which is expected to further narrow the laser linewidth by two orders of magnitude compared with the thermal atomic Faraday AOC to Hz level. Moreover, the four-level AOC based on the narrow linewidth cooling of Cs atoms using the 6S-7P transition is proposed. The 455 nm laser at 6S 1/2 -7P 3/2 transition plays two roles simultaneously, one is the cooling laser for a magneto-optical trap (MOT), another is the pumping laser for population inversion of 1470 nm clock transition, which is helpful to improve the compactness of the system. In the four-level structure, the frequency of pumping laser is far detuning from that of clock laser, therefore, the light shift resulting from the 455 nm laser is negligible. This four-level AOC based on cold atoms will further reduce the collision shift in thermal atom system to achieve a high-precision optical frequency reference.

In this work, we present the optimization of pumping light for Cs four-level active optical clock in detail. The relationships between the power stability of 1470 nm clock-transition laser and the power stability, as well as frequency stability, of 459 nm pumping laser are demonstrated, respectively. Through building an external cavity diode laser with power stability of $1\times 10^{-4}@ 1\ \mathrm{s}$ , the linewidth broadening of 1470 nm laser caused by power fluctuation of pumping laser is reduced to 43 Hz. Moreover, utilizing modulation transfer spectroscopy technique, the frequency stability of pumping laser is optimized by two orders of magnitude. Ultimately, the linewidth of 1470 nm active optical frequency standard is reduced to 120 Hz.

We have proposed a new scheme for the realization of an excellent active optical frequency standard by utilizing fast and slow twice cavity-locking technique in dual-wavelength active optical clock. The performance is expected to achieve the short term stability of $3.8\times 10^{-16}$ at 1 s and long-term stability of 10−18 magnitude. Also, the linewidth is expected to reach the quantum limited linewidth with the frequency shift of $7.1\times 10^{-5} \text{Hz}/\mathrm{s}$ . The system includes four main technologies: dual-wavelength active optical clock, Pound-Drever-Hall technique, phase-stabilized femtosecond laser comb and high speed feedback technique. The cavity length is relocked through slow and fast feedback to two piezoelectric translators of the main-cavity. Therefore, the residual cavity-pulling effect influencing the long-term frequency stability in four-level active optical clock can be suppressed by square times of the bad-cavity coefficient. The frequency stability and the frequency shift of the active optical frequency standard are expected to be two orders and four orders of magnitude better than the ultra-stable reference cavity laser, respectively.

The hyperfine structure (hfs) of Cs 7P 1/2 state is measured utilizing four-level active optical clock. Combing the Doppler effect and the active stimulated emission, the accuracy of Cs 7P 1/2 hfs is expected to be optimized. The correction terms of experimental results, such as cavity-pulling effect, light shift and collision shift, are analyzed. Such a scheme can be widely extended to other alkali-metal atoms to enrich the measurements of hfs.

This paper provides a feasible method to narrow the linewidth of the laser by modulation transfer spectroscopy, benefiting from a high feedback bandwidth and the high signal-to-noise ratio of the spectroscopy. We experimentally stabilize the frequency of a 420 nm blue diode laser with a free-running Lorentz linewidth of 43 kHz on the quantum transition of 85Rb, and the heterodyne experiments based on two identical configurations showing that the linewidth of laser is efficiently narrowed by 6 times, namely a Lorentz linewidth of 7 kHz. With the feedback bandwidth and signal-to-noise ratio in-loop further enhanced, the scheme with a relatively simple construction can potentially achieve a sub-kHz laser linewidth.

In this paper, we propose a chip-scale cesium four-level active optical clock based on a microfabricated atomic vapor cell. This millimeter-scale vapor cell is coated on both ends of the wall, and the coated walls directly construct the optical resonator. The microfabricated atomic vapor cell is also used to stabilize the frequency of the pump laser, to further reduce the influence of light shift caused by the frequency-stabilized pump laser on the linewidth of active optical frequency standard signal. We make a theoretical analysis and design an experimental scheme. The chip-scale active optical clock with small size and high performance has wide application in precision measurement and detection, and other fields, and it will aid to promote the definition of time unit second based on the optical clock.

We have experimentally demonstrated the active optical clock with a good suppression to cavity-length noise compared with the passive one. However, the frequency stability of the four-level active optical clock for thermal atoms is still limited by the residual cavity-pulling effect. In this paper, we preliminarily realized the cavity-length stabilization in 1064/1470 nm dual-wavelength good-bad cavity system. The synchronous cavity-length change between two dual-wavelength systems is realized by using the phase locking technique of 1064 nm good-cavity lasers. Therefore, the beating linewidth of 1470 nm bad-cavity lasers will also be reduced considering that the 1064/1470 nm dual-wavelength lasers share the one cavity. The tracking accuracy of 1064 nm good-cavity lasers is better than $3 \times 10^{-16}$ at 1s after phase-locking, and the linewidth of 1470 nm bad-cavity laser is reduced to 77 Hz. The linewidth of active optical frequency standard is still limited by the light shift, collision shift and Zeeman shift. The beating signal of magnetic sublevels corresponding to the Cs 1470 nm clock transition is observed under Zeeman effect. Further research is needed, such as, the design of vacuum chamber and magnetic shielding, to reduce the linewidth of the continuous 1470 nm active optical frequency standard.

Utilizing the modulation transfer spectroscopy (MTS) technique, we realize a compact pumping laser at 459 nm based on cesium (Cs) 62S 1/2 F=4 to 72p 1/2 F'=3 transition with a stability of 1. 8 $\times 10^{-14}/\sqrt{\tau}$ and decreasing to $8\times 10^{-15}$ at 60 s. The 459 nm pumping laser stabilized by MTS technique, achieves the stability by about 2 orders of magnitude better than that of the saturation absorption spectroscopy (SAS), which will contribute to the linewidth reduction of 1470 nm ultimate laser in Cs four-level active optical clock. The 1470 nm stimulated radiation can reach a power of $100 \ \mu\mathbf{W}$ with the stabilized 459 nm pumping laser power being 6 mW. Such a stable laser not only can be used as the pumping laser in active optical clock system, but also a novel optical frequency standard for length and other applications.

We experimentally realize a dual-wavelength good-bad cavity active optical clock based on the Nd: YAG crystal and cesium cell, of which the 1064 nm output signal as well as the Cs 1470 nm clock signal share a same cavity, and work in good cavity and bad cavity regime, respectively. We measure the detailed characteristics of the output signals. To further suppress the residual cavity pulling effect, we propose a preliminary cavity stabilization scheme where two independent systems are built and their good cavity signals are locked to each other, thus realizing the locking of cavity length. This scheme can demonstrate the technical readiness for the cavity stabilized dual-wavelength active optical clock that the main cavity is stabilized to a super cavity through PDH technique.

We propose a dual-wavelength good-bad cavity active optical clock, of which the two output signals with different wavelength share the same cavity, and work in good cavity and bad cavity regime, respectively. The good cavity signal is locked to a super cavity by the PDH technique, and thus the main cavity length of the active optical clock is stabilized. The frequency stability of the clock signal is expected to be improved by 2 orders of magnitude than that of the PDH stabilized signal, due to the suppression of cavity pulling effect in the bad cavity. Experimentally, we take the Nd: YAG 1064 nm transition as good-cavity gain medium, and the bad-cavity signal works on Cs 1470 nm transition. The dual-wavelength output of the active optical clock is realized, and the power and linewidth characteristics are preliminarily studied.

We propose an active all-optical magnetometer based on Cesium four-level atomic system. The magnetometer is free of radio frequency antenna, thus has smaller measure volumes. With an theoretical milli Hertz linewidth of the four-level active optical clock, the magnetometer has a potential sensitivity of tens of fT Hz−1/2.

In this paper, we get through some work to solve a detailed problem of the cesium active optical clock. With 459 nm laser pumping, the exact hyperfine energy levels between which the stimulated emission of Cs active optical clock takes place are studied.

We realize a Faraday anomalous dispersion optical filter (FADOF) operating on the 88Sr (5s2)1S 0 -(5s5p)1P 1 transition, utilizing a strontium hollow cathode lamp (HCL). At the magnetic field strength of 1460 G and the HCL discharge current of 22 mA, a single transmission peak with a maximum transmission of 28.8% is obtained. The dependence of transmission on magnetic field and HCL discharge current is qualitatively studied. This demonstration will be used to build a Faraday laser, which will be applied in the Sr optical clock.

The concept of active optical clock was proposed ten years ago. In this paper, after a simple review, we will mainly present the most recent experimental progresses of active optical frequency standards in Peking University, including 4-level Cesium active optical frequency standards and active Faraday optical frequency standards.

In this paper, we present a laser scheme without cavity in a 10 cm cesium cell as a potential active optical frequency standard. Since no cavity is applied, the stimulated light is emitted from the atoms directly and the center frequency of output laser light is solely determined by atoms without cavity pulling. The threshold characteristic of the emitted light is measured. This scheme can be used to investigate the relation between stimulated emission and amplified spontaneous emission. It is expected to be further extended to generate other narrow linewidth frequency standard signals.

We realize the lasing of cesium active optical clock with 459 nm laser pumping, which operates deep in the optical bad-cavity regime. The ratio between cavity bandwidth and gain bandwidth is 55.08 theoretically. With 459 nm laser pumping, the population inversion occurs between the cesium 7S 1/2 state and 6P 3/2 state, and the stimulated radiation between the two states is realized. The 1469.9 nm output signal of cesium active optical clock can reach a power of 8 μW. The output power also shows a threshold character with pumping laser power and can be influenced by the Cs cell temperature. This active optical clock has an advantage in stability over the conventional optical clocks, due to its suppression of cavity pulling effect, which is also demonstrated experimentally.

In order to develop small optical clock for various transportable applications with better stability and accuracy than that of commercial small Cs clock and H-maser clock, our group has proposed a small Ca atomic beam clock scheme with electron-shelving detection. Its potential stability was experimentally demonstrated recently. Here, we first demonstrated the dispersive detection of 657 nm transition via the Faraday rotation effect of 423 nm transition based on a thermal Ca atomic beam, this alternative detection method can effectively detect the clock signal by the ground state atoms after the clock laser interrogation. The Faraday anomalous dispersion optical filter of 423 nm transition can reach a maximum transmission of 10%. With a magnetic field of 84 G, the observed 3.3% of the ground state atoms has been excited to the σ± level of metastable 3P1(m=±1) state, which are separated 176.6 MHz to m=0 level.

We are setting up an experiment to investigate an active optical clock scheme in four-level configuration with Cesium atoms. The 1469 nm Cesium active optical clock output in a bad cavity laser regime is generated and the wavelength is measured to be 1469.500 nm by using spectrometer. The 1469 nm lasing threshold and output power is measured when changing 455 nm pumping laser power and frequency. The 1469 nm Cesium active optical clock output multi-threshold is observed when changing bad-cavity length. We also sweep the bad-cavity length and measure the 1469 nm Cesium active optical clock output frequency using a wavelength meter, proving the cavity-pulling reduction due to the bad-cavity effect.

The reliability of selecting the power lines of single-phase fault in small current grounding system is rather low because the fault current is too little, the electric arc is unstable, the electromagnetic interference is strong and the SNR is low. The paper utilized wavelet transform to extract the transient Special Frequency Band (SFB) of zero sequence voltage and current. Because the transient current directions between faulty feeders and healthy feeders are opposite in SFB, the transient Reactive Power algorithm is selected for the fault feeders selecting. The simulation and analysis by MATLAB verified that the proposed method can exactly distinguish single-phase grounding fault feeders and it has higher reliability and sensitivity.