The last decade has witnessed tremendous progress in research on optical frequency metrology. Optical frequency standards using single-ion trap technologies and optical lattice have reached stability and accuracy of 10-18 level [1,2]. Although the traditional passive optical clocks have reached a beautiful result, the limitation is still the Brownian thremal noise of high-fineness Fabry-Perot cavity for frequency stabilization of the oscillation laser. Moreover, the PDH laser system is also sensitive to the cavity noise, and the cavities with high performance and low operating temperature are complicated to realize. Reducing the linewidth to millihertz level is still a challenge. However, this formidable hurdle is cleared by the active optical clock [3,4], which is first proposed by Professor Chen of Peking University in 2005.
Active optical clock, utilizing optical stimulated emission on ultra-narrow atomic transition line in bad-cavity regime with coherent weak optical feedback to maintain collective phase information from different atoms, could greatly reduce the influence of the thermal vibrations of the cavity mirrors on the emitted optical frequency. Since the concept of active optical clock has been proposed, several experimental schemes [5-7] in different configurations have been demonstrated. In 2015 Joint Conference of the IEEE IFCS&EFTF, it was listed as one of the three most popular emerging technologies in the field. Moreover, the research group of JILA proposed that: such systems have the potential to improve the stability of the best clocks by about 2 orders of magnitude.
The throretical quantum limited linewidth of the active optical clock is narrower than mHz , and to reach this unprecedented linewidth is possible since the effect of thermal noise on cavity mode can be supressed dramatically with the cavity-pulling supression mechanism of active optical clock. Besides serving as a local oscillator in passive optical clocks schemes, it can also be applied as quantum frequency standards directly, due to the atomic frequency reference. In a word, the active optical clock has the potential to break the existing bottleneck of optical clocks.
Traditional optical clocks are based on the “passive mode” of operation, which means the laser frequency is locked to the very narrow atomic spectral line, but not the stimulated emission radiation frequency itself. As shown in the Fig.1, the cavity mode linewidth is much narrower than the laser gain profile, leading to the center frequency of a good-cavity gas laser or a super-cavity stabilized laser follows the cavity length variation almost perfectly to the level of mHz, thus the final technical limitations on the available laser linewidth are from the variations of the cavity length. The conventional optical clocks based soled on the absorption laser spectroscopy, while the active one based on the stimulated emission radiation which is very stable and can be used as a frequency standard. That is, active optical clock utilizes the bad-cavity with cavity mode whose linewidth is much wider than the laser gain profile. Since the output frequency is determined by a clock transition of perturbation-free atoms, it will provide long-term stability and accuracy as the current passive optical clock. Operating in the bad-cavity regime, the laser center frequency does not follow the cavity length variation exactly, but in a form of suppressed “cavity pulling” shift .
Fig.1. The working mechanism and bad cavity coefficient of the passive optical clock and the active one. (a) Traditional optical clock. (b) Active optical clock .
Different approaches has been tried to the creation of a high-stability active optical frequency standard. Such as, neutral atoms at 2-level, 3-level  and 4-level energy structures [11,12] with thermal and laser cooled and trapped configurations, Raman laser [13,14], sequential coupling configurations, and moving optical lattice have been investigated recently. The Raman laser in bad-cavity regime has been examined with cooled Rb atoms with a perfect result. However, the light shift due to pumping laser may be limitation of a high performance for active optical clocks with laser cooled and trapped atoms in 3-level configuration. There is also research group demonstrated and characterized stimulated emission from the millihertz linewidth clock transition in an ensemble of laser-cooled 87Sr atoms trapped within a high-finesse optical cavity . However, this ultranarrow optical transition can be only made to lase in a pulsed manner, which is currently not useful as a frequency reference，if there is no phase locking between pulses [16,17].
To resolve the problems existing above, we put forward the four-level active optical clock [11,12,18] early, which could reduce influences of pumping laser on lasing levels and emitted light frequency. It is worth mentioning that we have realized the 1470 nm stimulated emission of cesium (Cs) four-level active optical clock. The cavity-pulling suppression mechanism have also been examined. However, without any vibration isolation, the stability is still limited by the residual cavity pulling effect. This challenge can be moved by the 1064/1470 nm dual-wavelength good-bad cavity active optical frequency standard [19,20] which can stabilize the main cavity length with 1064 nm good-cavity laser. The relevant atomic energy levels of Nd:YAG crystal and Cs has shown in the Fig.2 . The Fig.3 has shown the experimental setup of 1064/1470 nm dual-wavelength good-bad cavity active optical standards, where cavity mirror M1 is coated with 808 nm anti-reflection and 1470&1064 nm high-reflection coating. M2 is coated with 459 nm anti-reflection and the reflectivity of 1470 nm and 1064 nm is 70% and 95%, respectively.
Using an integrated structure, the Nd:YAG 1064 nm and Cs 1470 nm output lasers with the gain bandwidth is 132 GHz and 10 MHz , share a common cavity and work in good-cavity regime and bad one, respectively. The output 1064 nm laser frequency, which is pumped by 808 nm laser with Nd:YAG as gain medium, will be locked to a super cavity at subhertz by PDH technique to stabilize the main cavity length . On the contrary, the 1470 nm output laser of bad cavity, is based on the stimulated emission radiation from Cs 72S1/2 to 62P2/3 level and realized by 459 nm laser pumping of Cs atoms in the cavity, as the ultimate output laser. Due to the effect of cavity pulling suppression mechanism in the bad cavity regime, the frequency stability of the 1470 nm output laser signal is expected to be improved by 2 orders of magnitude than that of the PDH stabilized 1064 nm good-cavity signal, and the theoretical quantum-limited bandwidth was calculated to 72.5 mHz under our experimental condition.
Fig.2. Relevant atomic energy levels. (a) Nd3+of Nd:YAG crystal. (b) Cesium.
Fig. 3. Experimental setup of 1064/1470 nm dual-wavelength good-bad cavity active optical standards
Through the preliminary exploration, we have realized the 1064/1470 nm dual-wavelength output in one integrated cavity, whose power are independently controlled by 808 nm and 459 nm pumping laser, and extracted separately through mirror coating. The output power is measured as shown in Fig. 4, the function curve of 1064/1470 nm output power depending on the 808/459 nm pumping power respectively, where the red line represents for the 1064 nm laser and the blue line for the 1470 nm laser. It has showed that the output power both increased with the growth of pumping power.
Fig. 4. Output power of 1064/1470 nm good/bad-cavity signal vary with the 808/459 nm pumping power.
(b) Linewidth charicteristic
We measure the output linewidth of the dual-wavelength signals by heterodyning between two identical experimental systems. The typical beating signals of the 1064 nm and 1470 nm lasers are respectively shown in Fig. 5. The 1064 nm signal has a beating linewidth of 15.4 kHz, thus the linewidth of a single laser is 10.9 kHz. For 1470 nm, the beating signal is 210 Hz, denoting that a single system has a linewidth of 149 Hz.
Fig. 5. Beating signal of the 1064/1470 nm good/bad-cavity signal.
The discrepancy between the linewidths of the two signals sharing the single cavity is that the 1470 nm signal works in bad-cavity regime, thus the fluctuations of the cavity mode influence its output frequency much more slightly than the 1064 nm good cavity signal, i.e. having the suppression of the cavity-pulling effect. To verify this mechanism in bad cavity we measure the frequency shift of the two signals by observing the beating signals’ movement, when tuning the cavity mode through a piezo ceramic element. As shown in Fig. 6., the frequency of 1064 nm good cavity signal changed exactly with the cavity mode, while for 1470 nm bad cavity signal, the cavity pulling is suppressed to about 1/65 of the cavity detuning. Thus the experimental measured bad cavity factor turns out to be 65, which agrees well with the theoretical one.
Fig. 6. Frequency shift of good/bad-cavity single depending on the cavity detuning.
Active Faraday optical frequency standards  utilize Faraday atomic filters [22-24] as frequency references when working in bad-cavity regime. The output light frequency is determined by alkali atomic transition line of Faraday atomic filter and the output stimulated emission light power can be increased by adopting Ti: sapphire, dye and semiconductor materials as gain medium since the quantum reference of frequency standard and the stimulated emission of gain medium are spatially separated. This unique approach of active optical clock opens the door for various atomic transitions and alternative gain media to optical clocks.
The Faraday atomic filters with narrow bandwidth have been studied in our group since 2011 [25-27]. The experimental setup of ultranarrow bandwidth Faraday atomic filter based on alkali atoms is shown in Fig. 5. It is realized by velocity selective optical pumping of alkali vapor in a bias magnetic field. The Faraday atomic filter is composed of two polarization-orthogonal Glan-Taylor prisms, an alkali vapor cell, a pumping diode laser with circular polarization and a bias magnetic field. The pumping laser is frequency stabilized to alkali atomic saturation absorption spectroscopy. The bandwidth of the Faraday atomic filter could reach 25 MHz with a transmission of 18% , which is adequately applied in active Faraday optical frequency standards.
Fig. 7. Experimental setup of active Faraday optical clock using ultranarrow bandwidth Faraday atomic filter.
3.2. Experimental result
(a) Power charicteristic
When a Faraday atomic filter was placed inside extended cavity of laser diode with anti-reflection coating, stimulated emission of active Faraday optical frequency standard can be realized by adjusting the extended cavity mirror. Fig. 6 shows the output light power varying with injection current of laser diode. When increasing the injection current, the refractive index of semiconductor is changed. The whole cavity length, which is the sum of the extended cavity length and the optical length of semiconductor, is changed accordingly. Therefore, there are multiple thresholds of the injection current. The maximum output light power can reach 75 μW.
Fig. 8. The varization of output light power while increasing the injection current of laser diode.
(b) Cavity-pulling effect
We have also checked cavity pulling effect in active Faraday optical frequency standard by beat the output light with pumping laser. It was found that when changing the extended cavity frequency within 350 MHz, the center frequency of the beat signal varied within a range of 40 MHz. Therefore, the cavity pulling coefficient is 11% which is reduced compared with common laser. That means the current system works in bad-cavity regime.
(c) Linewidth charicteristic
The output light frequency linewidth was measured by the heterodyne signal between two independent identical setups. The beat signal is shown in Fig. 9. The swept frequency range is 20 kHz within 200 ms and RBW 100 Hz. The data were fitted by a Gaussian profile, which indicates FWHM of the beat signal is 398 Hz. The linewidth for each setup can be deduced by the measured FWHM divided by 2, which is 281 Hz. The result is 19000 times smaller than the natural linewidth of the Cs 852 nm transition line and two orders better than frequency-stabilized laser with atomic filter working in goodcavity regime or interference filter. It indicates that active Faraday optical frequency standard working in bad-cavity regime can reduce influence of vibrations on frequency stability.
Fig. 9. The output light frequency linewidth of active Faraday optical frequency standard.
We proposed the concept of active optical clock twelve years ago. After a simple review, we have mainly presented the most recent experimental progresses of active optical frequency standards in Peking University, including 4-level Cesium active optical frequency standards, dual-wavelength active optical clock and active Faraday optical frequency standards.
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