Cold Atoms, Cold Molelcules, and Spectroscopy

当有相关的理论预测和实验结果时，对自然和物理过程的理解才能最有成效地进行。这项理论和计算工作建立在过去15到20年在利用激光冷却原子方面取得的实验进展的基础上。在足够冷的温度下，玻色子的集合可以占据最低的量子态，产生玻色-爱因斯坦凝聚，而两个费米子不能处于相同的量子态。然而，在一维中，如果密度足够低，玻色子和费米子系综都发生碰撞而没有穿透。正如吉拉多先生在1960年指出的那样，在这种状态下，玻色子的行为就像费米子。预测和实验可以测试理论模型，从而扩展对有效一维约束下冷原子动力学的理解。拟议工作的第二部分涉及目前开发实验方法的努力，而不是用于原子，而是用于简单分子。通常的实验方法是从冷原子开始，诱导它们在磁场中结合（“费什巴赫共振态”），然后激发这些松散结合的分子进入不同电子结构的更高状态，然后衰变为最低的分子振动旋转量子态，具有最小的平动能量。这种生产方法需要精确的分子能级知识，以便知道在哪里调整激光。这个小组的工作是提供这些数据，以找到从冷钠（Na）和钾(K)原子中产生冷NaK分子的最佳途径。这项工作涉及广泛的领域，包括量子信息科学和超冷能量下的化学反应。该小组将研究费米子和玻色子在一维低密度体系中的一维系综。最近的实验测试了各种条件下原子系综谐振势振荡频率的理论模型。这一理论将通过计算原子系综在一定密度范围内的行为得到扩展，当存在中心势垒时，会产生“双阱”势。在冷原子状态下，当量子波函数扩展以穿透可能的势垒时，可以通过势垒进行量子隧穿。但这将取决于原子密度，它决定了原子系综与玻色子或费米子的极限相似的程度。由于中间情况呈现出相当复杂的情况，预测和实验可以检验理论模型，从而扩展对有效一维约束下冷原子动力学的理解。对于玻色子，时间相关的Gross-Pitaevskii方程已经成功地模拟了各种条件下的动力学行为。对于费米子，就像在原子理论中一样，在每个基态中都有一个粒子的决定性波函数被使用。在玻色子和费米子极限之间的有效一维势的动力学计算只在特殊情况下进行，例如纯谐波势。最新的时变矩阵对角化方法将适用于动态过程。为了扩大一维冷原子理论的应用范围，也值得考虑流体力学方法，而不是通常的对小的偏离平衡的简化。目前通过费什巴赫共振态生产冷分子的工作主要局限于由钾和铷组成的分子。这些原子发生碰撞反应，生成钾和铷分子。由钠和钾组成的分子不存在这个问题，所以一些实验室正在研究制造冷NaK的方法。这项工作的目标是分析现有的光谱数据，以准确地模拟大量可能的中间分子能级，以选择从冷Na和K原子产生冷NaK分子的最佳途径。这种研究双原子分子能量结构的方法将实验数据与由数值势和自旋轨道耦合函数计算的能级直接拟合。这与传统的振动和旋转参数上的邓纳姆展开形成对比，后者对非摄动状态非常满意，但不容易用于表征单重态-三重态摄动效应。这种方法的动机是，单线态和三重态的混合在从典型的三重态费什赫共振态逐步形成单线态冷分子的过程中是至关重要的。

An understanding of nature, and of physical processes, proceeds most fruitfully when there are correlated theoretical predictions and experimental results. This theoretical and computational work builds on experimental advances achieved in the last 15 to 20 years, in exploitation of laser cooling of atoms. An ensemble of bosons, at cold enough temperature, can occupy just the lowest quantum state, producing Bose-Einstein condensation, while two fermions cannot be in the same quantum state. However, in one-dimension, if the density is low enough, both boson and fermion ensembles collide without penetration. As pointed out by M. Girardeau in 1960, in this regime bosons behave like fermions. Predictions and experiments could test theoretical models and thereby extend the understanding of cold atom dynamics in effective one-dimensional confinement. The second part of the proposed work relates to current efforts to develop experimental methods beyond those used for atoms, to simple molecules. The usual experimental approach is to start with cold atoms, induce them to combine in a magnetic field ("Feshbach resonance states"), then excite these loosely bound molecules into higher states of different electronic structure which can then decay into the lowest molecular vibrational-rotational quantum state, with minimal translational energy. This production method requires an accurate knowledge of molecular energy levels so as to know where to tune the lasers. This group's work has been to supply that data to find the optimum pathway for production of cold NaK molecules from cold sodium (Na) and potassium (K) atoms. This work is relevant to a broad range of areas including quantum information science and chemical reactions at ultracold energies.The group will study one-dimensional ensembles of fermions and bosons in one-dimension in the low density regiem. Recent experiments have tested theoretical models for oscillation frequencies of atomic ensembles in harmonic potentials under various conditions. This theory will be extended by performing calculations for the behavior of atomic ensembles over a range of densities when there is a central potential barrier, giving a "double-well" potential. In the cold atom regime when quantum wavefunctions extend so as to penetrate a possible barrier, there can be quantum tunneling through the barrier. But this will depend on the atomic density, which determines the extent to which the atom ensemble resembles either extreme limit of bosons or fermions. Because the intermediate cases present rather complicated situations, predictions and experiments could test theoretical models and thereby extend the understanding of cold atom dynamics in effective one-dimensional confinement. For bosons, the time-dependent Gross-Pitaevskii equation has successfully modeled dynamical behavior in a wide range of conditions. For fermions, a determinantal wavefunction with one particle in each basis state has been used, as in atomic theory. Dynamics calculations in effective one-dimensional (1D) potentials intermediate between bosonic and fermionic limits have been pursued only in special cases, such as a pure harmonic potential. Recent time-independent matrix diagonalization approaches to dynamical processses will be adapted. To extend the range of applications of theory for cold atoms in 1D, it is also worth considering hydrodynamic approaches without the usual simplification of small departures from equilibrium. Current work on the production of cold molecules via Feshbach resonance states has been limited primarily to molecules composed of potassium and rubidium. These atoms react on collision to make potassium and rubidium molecules. Molecules composed of sodium and potassium do not have this problem, so methods to produce cold NaK are being pursued in several laboratories. This work has been and will continue to have the goal of analyzing available spectroscopic data to accurately model a large number of possible intermediate molecular energy levels to select the optimum pathway for production of cold NaK molecules from cold Na and K atoms. This approach to diatomic molecular energy structure employs direct fits of experimental data to energy levels computed from numerical potentials and spin-orbit coupling functions. This is in contrast to the traditional Dunham expansions over vibrational and rotational parameters, which are quite satisfactory for unperturbed states, but which cannot easily be used to characterize singlet-triplet perturbation effects. This approach is motivated by the fact that singlet-triplet mixing is crucial in the stepwise formation of singlet cold molecules from typically triplet Feshbach resonance states.