# Development of Compact and Robust Physical System for Strontium Optical Lattice Clock
## 2 The Compact and Robust Physical System
We measured the correlation between various slower lengths and the trapped low-velocity atoms in the Blue MOT. When the slower length was reduced to 10 cm, which is 1/3 of that in a traditional laboratory physical package, we still trapped nearly \(3\times 10^{6}\,{}^{87}\)Sr atoms in the Blue MOT [35]. This result means that the short Zeeman slower could guarantee sufficient cold atoms in clock detection. Due to the shorter length of the slower, its weight and power consumption were also significantly reduced (mass of 3 kg, maximum power consumption of 19 W). We designed and implemented a compact MOT vacuum chamber for atomic cooling and detection. The MOT vacuum chamber had 15 CF 16 viewports, distributed in different directions, to facilitate the connection and integration with other optical and mechanical components. In Figure 2b, the top view illustrates the layout of the lasers and magnetic field coils within the MOT region. To achieve a flat configuration, most windows were positioned on the horizontal plane, with only three vertical windows--two for the vertical MOT beam and one for the ion-gettering pump (located outside the MOT center region). The diameter of the vacuum chamber is only 180 mm, which has a very high space efficiency. To reduce atom adhesion, the window facing the oven was made of sapphire. Figure 2c provides a cross-sectional view of the MOT vacuum chamber, cut along the black dashed line in Figure 2b, facing the atomic oven. The figure outlines the dimensions of the vacuum chamber, with a light pipe diameter of only 13 mm to reduce the distance between the anti-Helmholtz coils, achieving a high magnetic field gradient and low power consumption. The inner and outer diameters of the anti-Helmholtz coils are 46 mm and 86 mm, respectively, with minimum and maximum distances of 18 mm and 48 mm. At a current of 2 A, the magnetic field gradient at the MOT center reached 50 Gs/cm, accompanied by an average power consumption of only 6.8 W. No water cooling or heat sink was required, significantly simplifying the structure of the physical package. The compensation coils comprise three pairs of square coils, each with a side length of 100 mm. To reduce weight, the chamber was made of titanium alloy. Because all lasers incident the physical system via optical fibers, we designed a set of integrated optical setups to adjust the alignment and polarization of the incident beam, as shown in Figure 3a. To maintain beam pointing stability, we designed threaded holes on the chamber shell of the physical package to install the integrated optical setups. Furthermore, all optical mirror mounts were springless and devoid of adjustable knobs. To enhance comprehension, we have provided a detailed explanation of the integrated optical setups using the probe beam optical setup as an example. In Figure 3b, an exploded view of the probe beam optical setup is presented, illustrating the configuration of the springless mirror mounts. The 461 nm probe laser is coupled into a non-adjustable collimator (1) to collimate the beam. The collimated beam has a diameter of approximately 1 mm and passes through a half-wave plate (3) and a wedge prism (5), finally entering the MOTvacuum chamber via a 45\({}^{\circ}\) mirror (9). The half-wave plate and wedge prism are mounted on rotation mounts (4), allowing the adjustment of the polarization and beam direction of the probe laser. After adjustment, they are secured in place using a support bracket (7). Due to the limited adjustment range of the wedge prism, high precision is required during mechanical machining. Additionally, a pedestal was designed on the mainframe (6), where the angle of the 45\({}^{\circ}\) mirror mount (11) is adjusted by adding aluminum alloy shims of varying thickness to ensure the alignment of the laser with the atomic position (no shims are used in our system). As the repumping beam enters from the opposite side of the probe beam, a 0\({}^{\circ}\) mirror mount (8) was added on the mainframe to ensure the repumping beam can return along the same path.