We aim to reduce the temperature of cold atoms in a one-dimensional optical lattice, as this can remarkably enhance atomic coherence time and thereby improve the performance of applications like quantum simulation, optical lattice clocks, and quantum computing. In a one-dimensional optical lattice clock, atoms that have undergone two-stage Doppler cooling are confined within the lattice. The lattice has strong confinement only in the polarization direction and weaker confinement in the other two directions, which leads to radial heating effects. Moreover, since cold atoms occupy different motional states within the lattice and follow a Boltzmann thermal distribution, using a clock laser to probe the atoms confined in the optical lattice can result in inhomogenous excitation due to the dependence of motional states on Rabi frequency. This inhomogeneity reduces the indistinguishability of fermions, introduces additional collision frequency shifts, and weakens the coherence between the laser and the atoms, ultimately decreasing the detection time. Consequently, it becomes impossible to obtain narrow linewidth clock transition spectra with high signal-to-noise ratios, further affecting the stability of the optical lattice clock and the level of quantum control. Even at μK temperatures, the Doppler broadening can still reach tens of kHz. Cooling the atom ensemble using the damping force generated by standing wave fields can effectively reduce the temperature. To further lower the temperature of the atoms, various sub-Doppler cooling techniques are employed to cool the trapped atoms to their vibrational ground state, such as evaporative cooling and Raman sideband cooling. However, evaporative cooling requires long evaporation times and significant atomic loss, making it unsuitable for many applications. In contrast, the effectiveness of Raman sideband cooling can rival that of ion traps, making this cooling method widely applicable in optical clocks and optical tweezers. In this work, we apply optical molasses cooling and longitudinal Raman sideband cooling in a one-dimensional optical lattice to effectively lower the temperature of the cold atom ensemble and enhance coherence.

Based on the ⁸⁷Sr optical lattice clock, the atomic temperature is cooled to the μK level after two-stage laser cooling and is confined in a one-dimensional optical lattice with a trap depth of U=182E_r. Using three pairs of orthogonal 689 nm lasers, a standing wave field is formed. By adjusting the frequency and power, the optical molasses cooling further lowers the temperature under the influence of three-dimensional damping forces. For the prepared quantum reference system, an appropriate bias magnetic field is applied, making the energy level shift of ¹S₀ indistinguishable, while the energy level shift of ³P₁ is highly resolvable. At this point, a 698 nm cooling laser is applied along the polarization direction of the lattice light (+Z direction), with its frequency set to the red-detuned resonance frequency of the clock transition. This excites the atoms from the |¹S₀,|n〉 state to the |³P₀,|n-1〉 state. Due to the long lifetime of the excited state ³P₀ [151.4(48) s], atoms cannot spontaneously return to the ground state quickly enough for effective cooling. Therefore, a 679 nm repumping laser is used to pump the atoms from the ³P₀ state to the ³S₁ state, allowing spontaneous relaxation to ³P₂, ³P₁, and ³P₀ states. Only the ³P₁ state can spontaneously relax back to |¹S₀,|n-1〉. Thus, a 707 nm repumping laser is applied to pump the atoms from the ³P₂ state to the ³S₁ state, ensuring that all populations return to the ground state |¹S₀,|n-1〉 via the ³P₁ state. The entire cooling process lasts about 30 ms, with the sideband cooling light circulating 5 times to improve cooling efficiency. Finally, two 698 nm clock lasers probe the atoms, achieving the axial and radial clock laser resonant transitions between (5s²) ¹S₀(F=9/2)-(5s5p) ³P₀(F=9/2), with the radial clock laser acting for 5 ms.

Through the optimization of the frequency and power of the 689 nm laser, optical lattice cooling successfully reduce the radial temperature of the atoms from 14.6 μK to 8 μK (Fig. 2). Longitudinal sideband cooling further lowers the axial temperature of the atoms from 5.6 μK to 1.2 μK (Fig. 2), decreasing the average external vibrational quantum number from 0.82 to 0.02. By observing Rabi oscillations (Fig. 3), the combination of optical molasses cooling and sideband cooling improves the maximum excitation fraction from 0.85 to 0.95, reduces inhomogeneous excitation, and increases the coherence time of the laser and atoms. Additionally, by measuring the atom fractions under different trap depths (Fig. 4), we demonstrate that our method increases low-temperature atom number in the lattice. This effect contributes to achieving higher stability for optical lattice clocks under lower quantum projection noise (QPN), particularly for shallow lattice clocks.

Optical molasses cooling and longitudinal sideband cooling effectively reduce the axial temperature of ⁸⁷Sr atoms to 1/5 of the temperature without cooling while also lowering the radial temperature. After cooling, the average vibrational state of the atoms is 0.02, with over 98.4% of the atoms in the vibrational ground state. The maximum excitation fraction increases from 0.85 to 0.95, indicating that this cooling method enhances coherence. Moreover, remaining atom fraction under different trap depths also show that cooling increases the atomic population. This research helps improve coherence time and the atom number in shallow optical lattices, thus enhancing the performance of quantum applications such as optical lattice atomic clocks. This cooling method can also be extended to other atoms, including ¹⁷¹Yb, ¹⁹⁹Hg, and ¹¹¹Cd. In future work, high-power lasers and three-dimensional sideband cooling can be utilized to cool atomic temperatures to the tens of nK, enhancing atomic coherence and increasing the atom number in shallow lattices, thereby improving the level of quantum control.