† Corresponding author. E-mail:
Project supported by the National Natural Science Foundation of China (Grant Nos. 61775220 and 11803042), the Key Research Project of Frontier Science of the Chinese Academy of Sciences (Grant No. QYZDB-SSW-JSC004), and the strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB21030100).
We report a transportable one-dimensional optical lattice clock based on 87Sr at the National Time Service Center. The transportable apparatus consists of a compact vacuum system and compact optical subsystems. The vacuum system with a size of 90 cm× 20 cm× 42 cm and the beam distributors are assembled on a double-layer optical breadboard. The modularized optical subsystems are integrated on independent optical breadboards. By using a 230 ms clock laser pulse, spin-polarized spectroscopy with a linewidth of 4.8 Hz is obtained which is close to the 3.9 Hz Fourier-limit linewidth. The time interleaved self-comparison frequency instability is determined to be 6.3 × 10–17 at an averaging time of 2000 s.
At present, the uncertainty or instability of the atomic optical clocks[1,2] reaches 10–19, which is better than the existing microwave clocks by nearly two orders of magnitude.[3–7] As one of the candidates for the next-generation time-frequency standard, atomic optical clocks have been developed in many laboratories.[1,8–12] The optical clocks can be used for high precision tests of fundamental physics constants,[13,14] chronometric leveling-based geodesy,[15] gravitational wave detection,[16] topological dark matter hunting,[17] frequency metrology, and timekeeping.[18]
Most of the optical clocks are confined in laboratories due to their complicated and bulky experimental apparatuses, which limit the application of the optical clocks in scientific research and engineering. Therefore, it is necessary to design and develop more compact and transportable optical clocks, which have not only low instability and uncertainty, but also high operation reliability under different conditions[19,20] to promote the comparison of clock signals, especially intercontinental comparison, more accurate and cost-effective than satellite link and long-distance optical fiber link. Furthermore, the development of transportable clocks is highly conducive to the research on space optical clocks.[21]
To date, a number of groups have demonstrated the transportable optical clocks. In 2014, the transportable boson 88Sr optical lattice clock was developed by the Italian LENS team with a physical system size of less than 2.0 m3, a systematic uncertainty of 7.0 × 10–15, and an instability of 4.0 × 10–15 / τ1/2.[8] In 2017, the German Physikalisch-Technische Bundesanstalt realized a transportable 87Sr optical lattice clock with systematic uncertainty of 7.4 × 10–17 and instability of 1.3 × 10–15 / τ1/2, while the entire experimental system was reduced to a size of 2.2 m× 3 m× 2.2 m.[22] In China, the Wuhan Institute of Physics and Mathematics of the Chinese Academy of Sciences developed a transportable calcium ion optical clock in 2016. The systematic uncertainty is 7.8 × 10–17 and the instability is 2.3 × 10–14 / τ1/2.[23]
Considered as one of the promising candidates for the redefinition of a second of the international system of units (SI), the strontium optical lattice clocks are constructed at the National Time Service Center.[11] So far, the stationary 87Sr optical lattice clock has a frequency instability of 4.0 × 10–17 at an averaging time of 8000 s and uncertainty of 9.6 × 10–17.[24–26] Based on the stationary 87Sr optical lattice clock, we develop a transportable optical clock. In this paper, we introduce the progress of the transportable optical clock based on 87Sr. First of all, we miniaturize the vacuum system. At the same time, all the sub-optical systems are modularized and fiber-coupled into the vacuum system so that every part can be easily moved. Then a spin-polarized clock transition spectroscopy with a narrow linewidth of 4.8 Hz is obtained. Furthermore, we realize the closed-loop operation and measure the frequency instability using the time interleaved self-comparison method.
The vacuum system mainly includes an atomic oven, a Zeeman slower, and a science chamber for the magneto-optical trap (MOT), as shown in Fig.
The oven is heated to generate strontium atomic vapor. Then the atomic beam is high-collimated by a nozzle containing 50 capillaries (length: 15 mm, diameter: 0.2 mm). The atomic flux of the thermal atomic beam is about 5 × 1011 atoms/s at the oven temperature of 733 K. The atomic beam propagates along a homemade Zeeman slower which consists of eight independent coils with an approximately effective length of 18 cm.[27] With the combination of the Zeeman slowing laser and the Zeeman compensating magnetic field, the atomic velocity is reduced to a couple of tens meters per second. A sapphire window, which can prevent strontium vapor coating, is used for coupling the Zeeman slowing laser into the Zeeman slower effectively. The oven region and the MOT region are pumped by two ion pumps at speeds of 25 L/s and 45 L/s, respectively. During clock operation, the pressure in the oven region is 3.6 × 10–6 Pa and that in the MOT is 1.9 × 10–7 Pa.
The decelerated atomic beam is trapped by standard MOT technique at the center of the science chamber with fourteen CF16 optical windows, as shown in Fig.
Figure
The experimental arrangement for all laser beams coupled into the MOT is depicted in Fig.
To prepare atomic samples, the first stage cooling, the second stage cooling, and subsequent optical trapping in a one-dimensional (1D) lattice are performed.[11] To achieve the spectroscopy of the clock transition, the atoms are interrogated by a clock laser. Laser sources of six different wavelengths are used for the transportable optical clock according to the energy level structure of 87Sr.[11] The involved laser subsystems are miniaturized and modularized as follows.
In the first stage cooling, the atoms are three-dimensional magneto-optical trapped with the transition of (5s2)1S0(F = 9/2)–(5s5p)1P1(F = 11/2) corresponding to a wavelength of 461 nm. But the transition is not perfectly closed. In order to improve the efficiency of the first stage cooling, repumping lasers at 707 nm and 679 nm corresponding to the transitions of (5s5p)3P2–(5s6s)3S1 and (5s5p)3P0–(5s6s)3S1 are used to pump the atoms to the (5s5p)3P1 state, in which the atoms finally decay to the ground state.
A frequency-doubled 600 mW 461 nm laser (SHG-pro, Toptica) is employed in this stage. Figure
Two external cavity diode lasers (ECDL) at 679 nm and 707 nm are employed as the repumping lasers. Figures
For the second stage cooling, all the optical beams are produced in a compact module mainly containing a master laser and two slave lasers at 689 nm. The schematic of the 689 nm laser system is shown in Fig.
Utilizing the optical injection locking technique, the two slave lasers inherit the master laser’s properties including linewidth and instability. We use a confocal Fabry–Perot cavity with a 1.5 GHz free spectral range and a finesse of 120 to monitor the single-longitudinal-mode operation condition of the slave lasers. The output from slave laser 1, modulated by AOM9, is used as trapping light corresponding to the inter-combination transition of (5s2)1S0(F = 9/2)–(5s5p)3P1(F = 11/2) of 87Sr atoms. The slave laser 2, modulated by AOM11, is used as stirring light corresponding to the transition of (5s2)1S0(F = 9/2)–(5s5p)3P1(F = 9/2). The frequency difference between trapping light and stirring light is 1.46 GHz. The diameter of the 689 nm beams into the first-stage MOT is 10 mm. Figure
After the first stage cooling, the Zeeman slower is turned off and the MOT magnetic field gradient is reduced to 3 G/cm immediately. In order to cover a wide range of atomic velocities during the atom transfer process from the first-stage to the second-stage MOT, both wide line trapping and stirring laser beams for the second-stage MOT should be frequency-modulated at 50 kHz with a span of 3.4 MHz. The laser power is 2 mW for wide line trapping and stirring at each direction. In the wide line trapping and stirring phase of 100 ms, the MOT magnetic field gradient of 3 G/cm lasts for 10 ms and is linearly increased to 10 G/cm to compress the atomic cloud within 90 ms. Then we switch into the narrow line trapping and stirring to further reduce the temperature of the atomic clouds. The powers of each narrow line trapping beam and stirring beam are about 40 μW and 10 μW, respectively. The narrow line trapping and stirring last for 30 ms under the constant magnetic field gradient of 10 G/cm. The final transfer efficiency of atoms from the first-stage MOT to the second-stage MOT is approximately 10%. After the second stage of cooling, the atomic cloud has a size of about 0.6 mm with the number of 2.0 × 106 and a temperature of 4.4 μK.
For the 1D optical lattice trapping, we use a 1 W diode laser at the magic wavelength of 813 nm (TA-pro, Toptica)[29] which is fixed on a 50 cm× 45 cm breadboard. The lattice laser output is coupled into a single-mode polarization-maintaining fiber and focused into the center of the MOT with a 150 mm focus length lens. After reflected and shaped, the retro-reflected beam superposes with the incident beam to form a 1D lattice. The waist of the incident beam and retro-reflected beam is approximately 46 μm. In order to load atoms efficiently, the waist positions are overlapped with the atomic cloud exactly. When the power of the incident beam is 400 mW, the depth of the lattice is 21.1 μK, deep enough to trap atoms from the second-stage MOT. The experimental arrangement of the lattice trap is shown in Fig.
In the opposite direction of the 813 nm laser beam is the 698 nm clock laser beam corresponding to the transition of (5s2)1S0(F = 9/2)–(5s5p)3P0(F = 9/2). The 698 nm ECDL (Toptica) is locked to a 10 cm ULE cavity with the finesse of 4 × 105 by the PDH method. The linewidth is approximately 1 Hz.[11] The 698 nm laser is delivered to the MOT by a 10 m single-mode polarization-maintaining fiber. In Fig.
Both polarizations of 698 nm clock laser and 813 nm lattice laser input into the MOT are purified as linear in gravity direction by using two Gran–Taylor prisms.
After being loaded into the lattice, the atoms are interrogated by 698 nm clock laser with a pulse length of 80 ms and a power of 300 μW. We use a normalized electron-shelving detection technique[30] by applying a combination of 461 nm detecting light for atoms fluorescence on the ground state 1S0 and repumping light to repump the excited atoms back to the ground state. Then we can get the normalized excitation fraction at the frequency of the interrogation laser. By scanning the frequency of the clock laser with steps of 300 Hz, the resolved sideband spectroscopy of the clock transition is obtained as shown in Fig.
Since 87Sr has a nuclear spin I = 9/2, there are ten ground sublevel states. In order to increase the signal to noise ratio and excitation ratio, the atoms are pumped into stretched states of mF = +9/2 or mF = –9/2 using a weak polarized light in the direction of gravity. The frequency of the polarized light is resonant with transition (5s2)1S0(F = 9/2)–(5s5p)3P1(F = 9/2). During the spin polarization process, a group of three-dimensional compensating coils is turned on to remove the horizontal magnetic field and a weak bias magnetic field of about 100 mG is applied in the direction of gravity. Meanwhile, the 200 μW polarized light is turned on and lasts for 15 ms. The polarization of the polarized light is adjusted by a liquid crystal wave plate into σ + or σ –, and the atoms are prepared into the stretched state of mF = +9/2 or mF = –9/2. After completing spin polarization, the bias magnetic field in the direction of gravity is increased to 330 mG to separate the ground sublevels. Furthermore, we perform spin-polarized spectra[32] using a 30 nW interrogation laser with 180 ms pulse length, as shown in Fig.
The time interleaved self-comparison method, usually employed to measure the systematic frequency shift, is used to verify the frequency stability improvement of the transportable optical clock.[33,34] Figure
Figure
In summary, we have constructed a miniaturized and modularized transportable optical clock. Compared with the traditional stationary optical clocks, the transportable optical clock has a more compact design. The volume of the vacuum system is reduced to 90 cm× 20 cm× 42 cm and all optical subsystems are integrated on independent optical breadboards. Apart from the electronics, the whole setup has been constructed within a size of 0.65 m3. The spin polarization spectrum with a linewidth of 4.8 Hz is obtained, which serves as a reference for the closed-loop operation of the transportable optical clock. The frequency instability is 3.6 × 10–15/τ1/2 and reaches 6.3 × 10–17 at an averaging time of 2000 s measured by the time interleaved self-comparison method. After completing the uncertainty evaluation and measurement of the absolute frequency of the clock transition in the next step, the transportable optical clock is expected to perform frequency comparison with other clocks and precision measurement.
[1] | |
[2] | |
[3] | |
[4] | |
[5] | |
[6] | |
[7] | |
[8] | |
[9] | |
[10] | |
[11] | |
[12] | |
[13] | |
[14] | |
[15] | |
[16] | |
[17] | |
[18] | |
[19] | |
[20] | |
[21] | |
[22] | |
[23] | |
[24] | |
[25] | |
[26] | |
[27] | |
[28] | |
[29] | |
[30] | |
[31] | |
[32] | |
[33] | |
[34] |