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The research field of ultracold atoms has expanded from atomic and molecular physics to a variety of fields. Ultracold polar molecules have long range and anisotropic dipole-dipole interactions, and similar to atoms, can also be conveniently manipulated by laser and other electromagnetic fields. Thus, ultracold molecules offer promising applications such as ultracold chemistry, quantum simulation, and quantum information. However, due to the difficulty in creating ultracold ground state molecules, expanding the horizon of ultracold physics from atoms to molecules is still under development. In the past decade, many research groups have successfully created bi-alkali rovibrational ground state polar molecules using magneto association and stimulated Raman adiabatic passage (STIRAP). This paper presents a review of the recent progress including creating and manipulating ultracold molecules with this method, and the collision property of molecules at ultracold temperature.
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Keywords:
- ultracold dipolar molecule /
- dipolar interaction /
- ultracold chemical reactivity /
- quantum simulation
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图 1 电场诱导23Na87Rb分子产生的有效电偶极矩
Figure 1. The induced effective dipole moments of the first two rotational states versus the electric field (23Na87Rb).
图 2 极性分子在电场中可以产生电偶极相互作用
Figure 2. Dipole-dipole interaction between polar molecules in an external electric field.
图 3 (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
Figure 3. (a) Two-channel model for a Feshbach resonance; (b) formation of a weakly bound Feshbach molecule by magnetoassociation.
图 6 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
Figure 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.
图 7 (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
${{{X}}^1}{\Sigma ^ + }$ 和${a^3}{\Sigma ^ + }$ 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${{{X}}^1}{\Sigma ^ + }$ 态的底部; 作为受激拉曼转移中间态的能级为电子单重态${A^1}{\Sigma ^ + }$ 和三重态${b^3}\Pi$ 的混合态, 其超精细结构的劈裂可以被完全分辨Figure 7. (a) 23Na87Rb molecule potential energy curves and the two-photonRaman process forpopulation transfer,
${{{X}}^1}{\Sigma ^ + }$ and${a^3}{\Sigma ^ + }$ 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${A^1}{\Sigma ^ + }$ and${b^3}\Pi$ ), which hyperfine structure can be resolved; (c) two-photon spectroscopy of the 23Na87Rb vibrational ground state with two rotational states resolved.
图 8 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]
Figure 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].
图 9 通过质心振荡运动测量基态23Na87Rb分子的囚禁频率
Figure 9. Center-of-mass motion of the absolute ground-state molecules along the horizontal direction (Xc) and the vertical direction (Yc) in the optical dipole trap.
图 10 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]
Figure 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].
图 11 (a) 基态23Na87Rb分子在340 Gauss磁场中的超精细结构, 其中
$m_I^{{\rm{Na}}}$ 和$m_I^{{\rm{Rb}}}$ 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$m_I^{{\rm{Na}}}$ =$m_I^{{\rm{Rb}}}$ = 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]Figure 11. (a) The calculated hyperfine Zeeman structures of the lowest rovibrational level of NaRb molecule at 340 Gauss,
$m_I^{{\rm{Na}}}$ and$m_I^{{\rm{Rb}}}$ 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].
图 12 (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]
Figure 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].
图 13 (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
Figure 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 + 87Rb2 process 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.
图 14 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
$\beta$ ; (b) 几种不同情况下样品温度对$\beta$ 的影响[63]Figure 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].
图 15 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
Figure 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.
图 16 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]
Figure 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].
图 17 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
$\beta$ 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]Figure 17. Temperature dependence of
$\beta$ 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]. -
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