Frequency-stabilized lasers are essential in the study of cold atoms and cold molecules for applications, such as laser cooling^[1–3], high-resolution spectroscopy^[4], quantum gases^[5], quantum sensing^[3,6], and precision measurement and metrology^[7,8]. Researchers have developed various frequency stabilization techniques to meet the demands of these applications, including stabilization based on atomic/molecular transitions^[9,10], Fabry–Perot cavity^[11], reference lasers^[12], and optical frequency combs^[13]. Recently, the complexity of experimental setups has increased, necessitating the use of multiple lasers with different wavelengths for optical clocks^[1], Rydberg atoms^[14], and the laser cooling of molecules^[15]. Each laser must be frequency-stabilized within the experiment. However, many lasers cannot be directly stabilized using atomic/molecular spectroscopy. As a result, various methods have been devised for multiple wavelength frequency stabilization.

One such method involves locking the lasers to a high-precision wavemeter using an optical switch^[16]. This allows the lasers to be stabilized across a broad wavelength range. However, even with simultaneous calibration of the wavemeter, the stability typically exceeds the MHz level. The second method for frequency stabilization involves using an optical frequency comb, which can achieve stability below the kHz level. However, this approach requires sophisticated and expensive equipment. The third method utilizes an ultra-stable cavity or multiple cavities with a single ultra-stable spacer, employing offset sideband locking to achieve low drift and narrow line width^[17,18]. Nevertheless, it has been observed that frequency stability in a single cavity can be significantly compromised due to absorption by the coatings on the blue side^[17]. Another technique is to transfer stability from a stabilized laser, which is commonly used to transfer the frequency stability from a spectrum-locked laser or an ultra-stable laser. When the transfer cavity (TC) is in an ambient environment, the transfer-locked laser typically achieves MHz-level stability^[19]. However, mounting the transfer cavity with higher finesse in a vacuum can enhance stability down to the 10 kHz level^[20].

In a mercury optical lattice clock, it is necessary to adopt and stabilize five lasers at different wavelengths. The clock transition at 265.6 nm (S10→P30) is interrogated using an ultra-stable laser, frequency-quadrupled from a 1062.5-nm laser locked to an ultra-stable cavity with an approximate frequency drift of 4 kHz/day^[21]. Mercury atoms are laser-cooled at the S10→P31 transition with a 253.7-nm laser, derived from a high-power, narrow line width 1015-nm laser, where the natural linewidth is about 1.27 MHz^[22,23]. The magic-wavelength optical lattice is created using a 362.5-nm laser, frequency-doubled from a Ti:sapphire injection-locked 725-nm laser^[24]. To maintain the relative uncertainty of AC-Stark shift below 10−18, the stability and uncertainty of the optical lattice laser should be below 100 kHz. The natural line widths of the S31→P30,2 transitions for optical pumping are 3.3 MHz and 7.8 MHz at wavelengths of 405 nm and 546 nm, respectively. The 546-nm laser is frequency-doubled from a 1092-nm laser. Of these, only the 1015-nm laser can be directly stabilized using the atomic spectrum in a vapor cell^[25,26], while the others require stabilization with narrow linewidth and high stability, particularly the 725-nm laser.

In this study, we introduce a simple and robust transfer locking scheme for these four lasers using a single multi-wavelength transfer cavity and the ultra-stable 1062-nm laser^[27]. The transfer cavity is temperature-controlled within an airtight chamber. Utilizing the offset sideband Pound–Drever–Hall (PDH) locking method^[28], we first stabilize the transfer cavity to the ultra-stable laser. Subsequently, all lasers can be transfer-locked, achieving beat note line widths of 27 kHz and 17 kHz for the 1015-nm and 725-nm lasers, respectively. The frequency fluctuation of the transfer-locked 1015-nm laser remains 10 kHz during 2 hours of operation. This cost-effective and easy-to-operate, high-stability multi-wavelength transfer locking system is well suited for various applications requiring stable lasers, such as optical clocks, Rydberg atoms, the laser cooling of molecules, and quantum computation with neutral atoms.

The transfer cavity is crucial for multiple wavelength frequency stabilization. This custom-built plano-concave cavity features a 10-cm-long invar spacer. The flat mirror (M2) is affixed to a piezo transducer (PZT), enhancing its adjustability. The radius of curvature is −500mm for the concave mirror (M1), which establishes cavity waists of approximately 264 µm at 1092 nm, 260 µm at 1062 nm, 254 µm at 1015 nm, 215 µm at 725 nm, and 160 µm at 405 nm. The TC is housed within a temperature-controlled and airtight aluminum chamber, detailed in Fig. 1. The chamber is composed of three sections: a base plate, a top plate, and a central part, which includes windows and electric feed-through. To mitigate any etalon effects, two polished windows are tilted at a 5-degree angle, allowing for optimal optical access for all lasers. The chamber assembly, including the windows and electrical feed-through, is sealed with custom O-rings. The heat sink of the TC is temperature-controlled by two thermoelectric coolers (TECs) and an NTC thermistor, keeping temperature variation below 20 mK. The coating of the cavity mirrors is designed for high reflection to all target wavelengths, whose reflectivity is larger than 99.5% for the most demanding wavelengths at 1062 nm, 1015 nm, and 725 nm. Derived from the measured transmissive spectroscopy, the finesse of the TC is determined as 3480(±120) at 1062 nm, 2120(±120) at 725 nm, 1530(±40) at 1015 nm, 560(±10) at 405 nm, and 390(±10) at 1092 nm. Therefore, the line width is about 430 kHz, 710 kHz, 1 MHz, 2.7 MHz, and 3.8 MHz, respectively (see Table 1). The whole system is positioned on an optical board, which in turn is affixed to an optical table using six sorbothane feet.

Figure 2 presents the schematic diagram of the multiple wavelength frequency stabilization system. The system utilizes a 1062-nm ultra-stable reference laser, with its frequency noise significantly reduced to the thermal noise limitation of its 10-cm-long ULE ultra-stable cavity. The laser exhibits a line width of approximately 0.5 Hz and a frequency stability of about 10−15 at 1 s average time, and the linear frequency drift is about 4.2 kHz/day^[21]. The reference laser passes through two fiber electro-optical modulators (FEOMs, Conquer, KG-PM-10-10G) before it has been coupled into the transfer cavity with a polarization-maintaining fiber. The first EOM (FEOM-1) phase modulates the 1062-nm laser using a variable RF frequency to generate the offset frequency sidebands, while the second EOM (FEOM-2) employs a fixed RF frequency of 12 MHz to enable PDH locking of the transfer cavity. Through a fiber collimator, the 1062-nm laser beam is mode-matched using a telescope, and then passes through a half-wave plate (HWP), a polarization beam splitter (PBS), and a quarter-wave plate (QWP). The light reflected from the M2 mirror of TC-1 is sent to a photodiode (PD) through the QWP and the PBS, generating the PDH error signal from the AC output of PD-1. This signal is subsequently fed into a proportional-integral-differential (PID) servo, which adjusts the piezo on the M2 mirror to maintain frequency stability. All the slave lasers are external cavity diode lasers (ECDLs) with Littrow configuration, using current modulation for PDH locking. The slave lasers at 1092 nm, 1015 nm, and 725 nm are all home-built ECDLs, while the 405-nm laser is a commercial ECDL (Moglabs, ECD004). The 1092-nm and 1015-nm lasers are combined into the same fiber as the 1062-nm laser using a fiber combiner, sharing the same optics and photodiode. To discriminate the PDH signal from the shared photodiode, each laser is modulated at a distinct frequency and set higher than the low-pass filter bandwidth in the PDH circuit (20 MHz for the 1015-nm laser and 15 MHz for the 1092-nm laser). The fast feedback from the PID servo is used to tune the current of the laser diode, while the slow feedback is used to tune the PZT on the grating. The 725-nm laser and the 405-nm laser are coupled into the TC using low-pass dichroic mirrors (LBTEK, DM10-950LP and DM10-650LP), respectively. The frequency stabilization of the PDH locking for the 725-nm laser, 1092-nm laser, and 405-nm laser is similar to the 1015-nm laser. The input power of the TC is between 10 µW and 100 µW for each laser.

The transfer cavity is offset sideband locked at the frequency of a 1062-nm ultra-stable laser^[29], with variable sideband modulation produced by a signal generator (Aeroflex 2023B). This method offers the flexibility of selecting the locking frequency, which proves beneficial for compensating drifts in the reference laser or setting the frequency for slave lasers. A typical sideband PDH error signal is shown in Fig. 3, with 260 MHz phase modulation in FEOM-1. The signal-to-noise ratio (SNR) of the sideband error signal is about 140, and the peak-to-peak amplitude is about 1.2 V. When the transfer cavity is in a locked state, the RMS amplitude stabilizes at around 17 mV, corresponding to a frequency variation of 13.5 kHz.

To evaluate the frequency stability of the transfer-locked lasers, we constructed two such cavities, designated as TC-1 and TC-2. The 1062-nm laser beam is split to these two TCs, enabling each to lock on a chosen sideband. Two 1015-nm ECDLs (SL-2 and SL-3) are locked on the TCs, respectively, and beat on a home-made photodiode with a bandwidth of 500 MHz. The beat note signal is monitored by a spectrum analyzer (Rigol, DSA815) and a frequency counter (Keysight, 53230A) with a bandwidth of 350 MHz. The Lorentzian line width of the beat note signal is about 27 kHz. Similarly, the beat note signal between two 725-nm lasers displays a Lorentzian line width of about 17 kHz. When we select the proper sideband frequency, the beat note frequency can be measured by the frequency counter. During 2 hours of measurement, as shown in Fig. 4, the beat note frequency fluctuates below 10 kHz when TC-1 and TC-2 are locked on the ultra-stable laser. However, if TC-2 is unlocked at the 1062-nm ultra-stable laser, the beat note frequency exhibits variations as large as 4.2 MHz over 2 hours, primarily due to thermal fluctuations of 20 mK for the invar spacer. These observations confirm that transfer locking effectively transfers the stability from the reference laser to the locked lasers at the 10 kHz level and compensates for frequency drift caused by thermal expansion of the invar spacer.

Temperature variations significantly affect the frequency stability of transfer-locked lasers, particularly because the transfer cavity does not operate in a vacuum environment. This results in an index of refraction slightly above unity, approximately 1.0003, depending on the temperature and pressure of the sealed air within the cavity. Such dispersion is a critical factor in the frequency stability of transferred signals. Figure 5 illustrates the effect of temperature on frequency stability. When two 1015-nm lasers are locked using TC-1 and TC-2, respectively, the temperature control of TC-2 is deliberately deactivated, and then the beat note frequency exhibits a drift of approximately 1.2 MHz corresponding to a 3 K temperature drift at the heat sink over 4 hours. This experiment indicates that the air density will slightly change the dispersion coefficient of the lights at different wavelengths. Thus, maintaining a controlled temperature environment is essential for enhancing frequency stability in transfer locking systems. A temperature variation of 20 mK can lead to a frequency variation of nearly 8 kHz.

To compare with the frequency stability on atomic spectrum locking, we introduce the third 1015-nm ECDL (SL-1), which is frequency stabilized on the frequency modulated saturated absorption spectroscopy (FMSAS) in a mercury vapor cell after amplified and frequency quadrupled to 253.7 nm^[12]. As shown in Fig. 6, when SL-1 is frequency stabilized using FMSAS of Hg202 atoms, the beat note frequency between SL-1 and SL-2/SL-3 exhibits variations of approximately 15 kHz and 59 kHz over 2 hours, respectively. Our frequency measurements are not conducted simultaneously so the beat notes of “SL-1 and SL-2” and “SL-1 and SL-3” are different. Moreover, comparatively, transfer locking demonstrates superior stability for the 1015-nm lasers, as the frequency stabilization of SL-1 via FMSAS is notably affected by the input power of 253.7 nm in the mercury vapor cell, atomic temperature, and other factors. As shown in Fig. 7, the short-term stability of SL-2 and SL-3 is better than that of SL-1, more than one order of magnitude at 1 s averaging time, and it is less than 10−12 at 0.1 s. Additionally, the long-term frequency stability of SL-2 and SL-3, at 5×10−12 exceeds over 100 s that of SL-1 by a factor of more than 2.

Furthermore, the SL-2 laser is adopted to measure the saturated absorption spectroscopy of the Hg202 atoms in a vapor cell. Frequency sweeping is achieved by slowly scanning the sideband frequency of FEOM-1, with a step frequency of 200 kHz for the 1062-nm light and a dwell time of 500 ms for each step. As shown in Fig. 8, despite the evident amplitude noise in the SAS, the SNR of the error signal remains remarkably high compared with the scanning of laser frequency directly. This approves the high-frequency stability of SL-2 through transfer locking. Moreover, the stability of the 1015-nm laser stabilized by the transfer cavity has already reduced below one-tenth of the line width required for the cooling light, and the line width of the mercury atoms cooling light is in the MHz level. Therefore, it is suitable for applications such as laser cooling of mercury atoms.

Here, we present a multiple wavelength frequency stabilization system with a single transfer cavity for a mercury optical lattice clock, which can offset sideband transfer lock four lasers from the 1062-nm ultra-stable laser. The temperature-controlled transfer cavity, housed within an airtight chamber (though not within a vacuum), effectively mitigates the effects of temperature-induced dispersion variation. Key to this system is the adoption of a wide-bandwidth fiber EOM to adjust the frequency setpoint. With the transfer cavity locked on the 1062-nm laser, the beat note line width is 27 kHz for two 1015-nm lasers and 17 kHz for two 725-nm lasers. The fluctuation of the transfer-locked 1015-nm laser is less than 10 kHz, outperforming the laser locked on the saturation absorption spectroscopy in a mercury vapor cell. Moreover, the transfer-locked 1015-nm laser is used to demonstrate the frequency modulation spectroscopy with a high SNR. Therefore, it can be suitable for the laser cooling of mercury atoms.

The compact transfer locking scheme, employing dichroic mirrors and differential modulation frequency, remains robust against variations in input power and the presence of multiple lasers, while providing ease of frequency adjustment for each laser through offset sideband PDH locking. Notably, the versatility of the system extends to the adjustability of the 1015-nm laser frequency using FEOM-1. Additionally, the incorporation of appropriate fiber EOMs or other high-bandwidth EOMs for the 725-nm, 1092-nm, and 405-nm lasers enables precise frequency control for all lasers in future applications. With a high stability of 5×10−12 over 100 s, the 1015-nm laser and 725-nm laser meet the requirements for the laser cooling and the magic-wavelength optical lattice, particularly for the mercury optical lattice clock. This kind of multiple wavelength frequency stabilization system is quite suitable for experiments for optical clocks, Rydberg atoms, and molecular cooling, which require multiple narrow line width continuous-wave lasers.