本論文發表7鋰133銫費什巴赫共振的耦合頻道計算。內容如下:一,巴赫共振的原理與超冷原子碰撞的複習。二,我們實驗的陳述。實驗中在 1000 G 以下觀測到六個 s- 波共振以及四個 p- 波共振,並使用有限溫度模型從原子損失量的數據取出共振位置。三,使用 MOLSCAT 和 BOUND 執行 7 鋰 133 銫費什巴赫共振的耦合頻道計算,算出散射長度、散射矩陣、以及束縛能量。鋰銫的位能可修正並符合實驗中觀測到的共振位置。從修正完畢的鋰銫位能計算,單態與三重態的散測長度為 a1 = 45.82(2)a0 與 a3 = 873.8(70) a0 。最後,鋰銫費什巴赫分子的散射長度與束縛能量由 MOLSCAT 和 BOUND 得著。
做出鋰銫完善的特徵調查,對未來使用7鋰133銫的研究是重要的。在近於磁性費什巴赫共振的區域,僅調磁場就可以鋰銫的交互作用強度調變數個數量級。費什巴赫共振的存在給予我們許多研究的可能性,如少體物理中的費什巴赫分子與葉菲莫夫三聚體,以及多體物理中的極子和單元量子氣體。

This thesis presents coupled-channel calculations of 7 Li-133 Cs Feshbach resonances. First, the principles behind Feshbach resonances and ultracold atomic collisions are reviewed. Then, the details of our experiment are elaborated. In this work, we observe six s-wave and four p-wave resonances under 1000 G, and the resonance positions are extracted from the loss profile with finite-temperature model fits. After that, coupled-channel calculations are carried out, using MOLSCAT and BOUND. In the calculations, the LiCs potentials are tweaked to fit the observed resonance positions. From the refined Li-Cs potentials, the singlet and triplet scattering lengths are calculated to be a1 = 45.82(2) a0 and a3 = 873.8(70) a0 . Finally, using MOLSCAT and BOUND, we also obtain the scattering lengths and binding
energies of the Li-Cs Feshbach molecules.
The full characterization of Li-Cs interaction is crucial to future research using 7Li-133Cs mixtures. Near the magnetic Feshbach resonances, it is possible to tune the Li-Cs interaction strength over several orders of magnitude, simply by varying an external magnetic field. The presence of Feshbach resonances in Li-Cs mixtures opens up exciting opportunities to explore few-body physics, such as Feshbach molecules and Efimov trimers, and many-body phenomena, such as polarons and unitary quantum gases.

1. Feshbach Resonance 5
1.1 Scattering of Two Particles 5
1.2 Hyperfine Interaction 8
1.3 Two-Channel Scattering Model 13

2 Experiment 16
2.1 Magneto-Optical Traps of Li and Cs 17
2.2 Optical Dipole Trap 17
2.3 Evaporation and Spin Preparation 18
2.4 Magnetic Feshbach Spectroscopy 21
2.5 Magnetic Field Error 21

3 Coupled-Channel Calculation 23
3.1 MOLSCAT 23
3.2 BOUND 25
3.3 Potential Shift 26
3.4 Computational Time-Cost 28
3.5 Thermal Averaging 29
3.6 Finite-Temperature Model Fit 34

4 Related Collisional Properties 38
3.7 Inelastic Two-body Loss 38
3.8 Resonance Strength 40
3.9 Singlet and Triplet Scattering Lengths 41

5 Conclusion 44

References 46

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