Fig. 1. The induced effective dipole moments of the first two rotational states versus the electric field (²³Na⁸⁷Rb). 电场诱导²³Na⁸⁷Rb分子产生的有效电偶极矩

Fig. 2. Dipole-dipole interaction between polar molecules in an external electric field.极性分子在电场中可以产生电偶极相互作用

Fig. 3. (a) Two-channel model for a Feshbach resonance; (b) formation of a weakly bound Feshbach molecule by magnetoassociation.(a)Feshbach共振的两通道模型; (b)利用Feshbach共振进行磁缔合产生弱束缚分子

Fig. 4. Creation of ²³Na⁸⁷Rb Feshbach molecule via magnetoassociation: (a) The magnetic field sequence; (b) absorption images of ²³Na and ⁸⁷Rb with and without dissociation procedure^[52]. 利用磁缔合制备²³Na⁸⁷Rb Feshbach分子 (a)磁场改变的时序; (b)分别在离解和不离解的情况下探测钠和铷原子^[52]

Fig. 5. Binding energy of ²³Na⁸⁷Rb Feshbach molecules versus magnetic field near 347.7 Gauss. The inset shows the closed-channel fraction of the Feshbach molecule versus magnetic field^[52]. ²³Na⁸⁷Rb Feshbach分子的结合能随磁场的变化, 插图表示离共振越远, 分子的closed channel成分越多^[52]

Fig. 6. Electric-dipole moment of heteronuclear molecules as a function of internuclear distance (a₀ is the Bohr radius). The red up-pointing triangle is ²³Na⁸⁷Rb molecule. 异核碱金属双原子分子的电偶极矩和核间距(a₀为玻尔半径)的关系, 图中红色空心三角为²³Na⁸⁷Rb分子

Fig. 7. (a) ²³Na⁸⁷Rb molecule potential energy curves and the two-photonRaman process forpopulation transfer, and are the lowest singlet and triplet state respectively; (b) high resolution one-photon spectrum of the transition from the Feshbach state to the intermediate level (singlet and triplet mixed vibrational levels of and ), which hyperfine structure can be resolved; (c) two-photon spectroscopy of the ²³Na⁸⁷Rb vibrational ground state with two rotational states resolved. (a) ²³Na⁸⁷Rb分子的相关势能曲线; (b)分子中间激发态的超高分辨谱; (c)基态转动能级; 其中 和 为电子的最低单重态和三重态, Feshbach分子处于这两个态的离解极限附近, 而振转基态则处于 态的底部; 作为受激拉曼转移中间态的能级为电子单重态 和三重态 的混合态, 其超精细结构的劈裂可以被完全分辨

Fig. 8. Creation of ²³Na⁸⁷Rb molecules in the rovibrational ground state via STIRAP: (a) Time evolution of the ²³Na⁸⁷Rb Feshbach molecule number during a round-trip STIRAP, the reversed STIRAP is necessary for detection; (b) the pump and dump beam Rabi frequency during the STIRAP pulse sequence^[50]. 利用STIRAP制备²³Na⁸⁷Rb基态分子 (a) STIRAP过程中Feshbach分子数目随时间的变化; (b)同一实验中pump和dump激光器的拉比频率随时间的变化; 为了探测基态分子, 需要一个逆过程将分子从基态转移回Feshbach 能级^[50]

Fig. 9. Center-of-mass motion of the absolute ground-state molecules along the horizontal direction (X_c) and the vertical direction (Y_c) in the optical dipole trap. 通过质心振荡运动测量基态²³Na⁸⁷Rb分子的囚禁频率

Fig. 10. Stark shift of the rovibrational ground state ²³Na⁸⁷Rb molecule in electric field. The red curve is the fit to a model including contributions from several higher rotational levels. The inset shows the induced dipole moment vs the electric field with the currently accessible region marked by the shading area^[50]. 基态²³Na⁸⁷Rb分子在直流电场中的Stark频移. 红色曲线为对数据点的拟合. 插图为有效电偶极矩和电场的关系^[50]

Fig. 11. (a) The calculated hyperfine Zeeman structures of the lowest rovibrational level of NaRb molecule at 340 Gauss, and are nuclear spin projection of ²³Na and ⁸⁷Rb respectively; (b) two-photon spectrum obtained by dark resonance spectroscopy with six of the 16 hyperfine levels fully resolved^[50]. (a) 基态²³Na⁸⁷Rb分子在340 Gauss磁场中的超精细结构, 其中 和 分别为²³Na和⁸⁷Rb原子核自旋的磁量子数, 能量最低的超精细结构为 = = 3/2的态(最右端); (b) 利用仔细选择的STIRAP参数, 可以充分分辨跃迁允许的所有超精细结构, 从而实现处于单一超精细能级分子的制备^[50]

Fig. 12. (a) ²³Na⁸⁷Rb molecule rotational states with J = 0, 1 consist of different nuclear spin components; (b) coherent manipulation with microwave pulses shows the observed Rabi oscillations for the three microwave transitions in (a)^[59]. (a) ²³Na⁸⁷Rb分子的J = 0和J = 1转动态具有不同核自旋态的成分; (b)利用单光子微波(上), 和双光子微波(中和下)操控, 可以实现对转动能级和核自旋的操控^[59]

Fig. 13. Schematic energy-level diagram for chemical reactivity of (a) ⁴⁰K⁸⁷Rb molecules and (b) ²³Na⁸⁷Rb molecules. The schematic reaction coordinates for the ⁴⁰K⁸⁷Rb + ⁴⁰K⁸⁷Rb → ⁴⁰K₂ + ⁸⁷Rb₂process is exothermic and thus allowed. But the same process is endothermic for ²³Na⁸⁷Rb and thus forbidden. For ²³Na⁸⁷Rb in the first excited rovibrational level (v = 1, J = 0), the same reaction is already exothermic and thus allowed. (a) ⁴⁰K⁸⁷Rb分子和(b) ²³Na⁸⁷Rb分子体系两体反应的相关能级示意图, 两个基态⁴⁰K⁸⁷Rb分子间可以发生(6c)式中的化学反应, 两个基态²³Na⁸⁷Rb分子是化学稳定的, 将²³Na⁸⁷Rb分子制备到振动激发态, 可以允许化学反应发生

Fig. 14. Inelastic collisions of fermionic ⁴⁰K⁸⁷Rb molecules in the rovibronic ground state: (a) Sample data shows the time dependence of the molecule number density, the solid line is the fit based on a two-body decay model; (b) loss rate coefficient versus temperature^[63]. 基态费米⁴⁰K⁸⁷Rb分子的碰撞研究 (a) 分子密度随时间的变化, 红色曲线为用(7)式做的两体损耗拟合, 从中可以提取出损耗速率常数 ; (b) 几种不同情况下样品温度对 的影响^[63]

Fig. 15. Universal model of the ultracold molecule reactivity: (a) Identical fermionic molecules react via p-wave scattering and the rate of chemical reactions is determined by the p-wave angular momentum barrier; (b) non-identical fermionic molecules and identical bosonic molecules react via s-wave scattering.超冷化学反应的普适模型 (a) 全同费米分子通过p-波散射, 在长程有一个角动量引起的势垒; (b)非全同分子或全同玻色分子可以通过s-波散射, 没有长程势垒

Fig. 16. Inelastic collisions with different chemical reactivities of ²³Na⁸⁷Rb molecules. Time evolutions of (a) molecule numbers and (b) temperatures for both nonreactive (v = 0, J = 0)(filled circles) and reactive (v = 1, J = 0) (filled squares) samples in optical dipole trap. The blue dashed and redsolid curves are fitting resultsofmolecule number and temperature using Eq. (9)^[68]. 化学稳定(v = 0, J = 0)和有化学反应(v = 1, J = 0)的²³Na⁸⁷Rb分子在光阱中的损耗(a)和加热(b), 图中的曲线由通过对分子数目和温度同时拟合获得^[68]

Fig. 17. Temperature dependence of for chemical stable (v = 0) and chemical reactivity state (v = 1) of ²³Na⁸⁷Rb molecules. Theoretical curve based on the CC calculation are also shown. Four-atom collision complex formation is one of the possible mechanism of molecule loss for non-reactive molecules^[68]. 化学稳定(v = 0)和有化学反应(v = 1)的²³Na⁸⁷Rb分子在光阱中的损耗速率常数 与温度的关系, 图中的理论曲线为基于普适模型计算的结果. 在化学稳定的情况下, 可能的损耗通道为形成四体复合物(four-body complex)^[68]