Cold Atoms, Cold Molelcules, and Spectroscopy

冷原子、冷分子和光谱学

• 批准号: 1403160
• 负责人: Thomas Bergeman
• 金额: $ 7.5万
• 依托单位: SUNY at Stony Brook
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-09-01 至 2017-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1403160&HistoricalAwards=false
• 关键词: Cold; Atoms; Molelcules; Spectroscopy

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.

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就会取得最大的成果。这项理论和计算工作建立在过去15到20年来在利用激光冷却原子方面取得的实验进展的基础上。一个玻色子系综，在足够低的温度下，可以只占据最低的量子态，产生玻色-爱因斯坦凝聚，而两个费米子不可能处于相同的量子态。然而，在一维空间中，如果密度足够低，玻色子和费米子系综会在没有穿透的情况下发生碰撞。正如M.Girardeau在1960年指出的那样，在这个体系中，玻色子的行为就像费米子。预测和实验可以检验理论模型，从而扩展对有效一维约束中冷原子动力学的理解。拟议工作的第二部分涉及目前开发用于原子和简单分子以外的实验方法的努力。通常的实验方法是从冷原子开始，诱导它们在磁场中结合(“Feshbach共振态”)，然后将这些松散束缚的分子激发到不同电子结构的较高态，然后再衰变到最低的分子振动-转动量子态，平移能量最小。这种生产方法需要对分子能级有准确的了解，以便知道在哪里调整激光器。该小组的工作是提供这些数据，以找到从冷的钠(Na)和钾(K)原子生产冷的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。该小组将在低密度区域研究一维费米子和玻色子的一维系综。最近的实验已经验证了原子系综在不同条件下的振荡频率的理论模型。这一理论将被扩展，当存在中心势垒时，通过计算原子系综在一定密度范围内的行为，给出“双势垒”势。在冷原子区域，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，原子密度决定了原子总体与极端玻色子或费米子的相似程度。由于中间情形呈现了相当复杂的情况，预测和实验可以检验理论模型，从而扩展了对有效一维约束中冷原子动力学的理解。对于玻色子，含时的Gross-Pitaevskii方程已经成功地模拟了广泛条件下的动力学行为。对于费米子，就像在原子理论中一样，使用了每个基态都有一个粒子的行列式波函数。有效一维(1D)势介于玻色子和费米子极限之间的动力学计算仅在特殊情况下进行，如纯谐振势。最近用于动态过程的独立于时间的矩阵对角化方法将被采用。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，而不是通常简化对平衡的小偏离。目前通过费什巴赫共振态产生冷分子的工作主要局限于由钾和Rb组成的分子。这些原子在碰撞时发生反应，生成钾和锶分子。由钠和钾组成的分子没有这个问题，所以几个实验室正在探索产生冷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，以选择从冷的Na和K原子产生冷的NaK分子的最佳途径。这种对双原子分子能级结构的方法利用了实验数据与由数值势和自旋-轨道耦合函数计算出的能级的直接拟合。这与传统的关于振动和转动参数的Dunham展开式不同，传统的Dunham展开式对于非微扰态是非常令人满意的，但不容易用来表征单重态-三重态的微扰效应。这种方法的动机是这样一个事实，即单态-三态混合在从典型的三态Feshbach共振态逐步形成单态冷分子的过程中是至关重要的。