Multichannel Quantum Defect Theory (MQDT) is shown to be capable of producing quantitatively accurate results for low-energy atom-molecule scattering calculations. With a suitable choice of reference potential and short-range matching distance, it is possible to define a matrix that encapsulates the short-range collision dynamics and is only weakly dependent on energy and magnetic field. Once this has been produced, calculations at additional energies and fields can be performed at a computational cost that is proportional to the number of channels N and not to N^3. MQDT thus provides a promising method for carrying out low-energy molecular scattering calculations on systems where full exploration of the energy- and field-dependence is currently impractical.
We present a general formulation of multichannel quantum-defect theory (MQDT) for anisotropic long-range potentials. The theory unifies the treatment of atomic and molecular interactions of all types, and greatly expands the set of interactions that can be treated and understood systematically, including complex interactions involving molecules. In one exemplary manifestation, the theory provides a methodology to make the classification of atomic interactions based on the Periodic Table quantitative, instead of qualitative, and to generalize the Table to include molecular classes. Through the …
Multichannel quantum-defect theory for magnetic Feshbach resonances in heteronuclear group I systems
本文提出了一个多通道量子亏损理论，研究了两个I族杂原子相互作用中的磁费什巴赫共振。该理论提供了一个统一的和统一的描述共振在所有的分波，并使大量的共振的表征方面非常少的参数。对于$^6$ Li $^{40}$ K的样品系统，我们描述了在$aa$、$ab$和$ba$通道中、在分波$s$（$l=0$）到$h$（$l=5$）中以及在0到1000高斯的磁场中的所有共振。所有的共振，包括那些在非零分波，充分的特点是使用新开发的参数化高[物理。Rev. A \textbf{84}，022706（2011）]。
Quantum Defect Theory description of weakly bound levels and Feshbach resonances in LiRb
应用多通道量子亏损理论（MQDT）结合框架变换（FT）方法来模拟$^{7}$ Li $^{87}$ Rb和$^{6}$ Li $^{87}$ Rb的Fano-费什巴赫共振[Marzok { \it et al.} A { \bf 79} 012717（2009）]。MQDT的结果显示出的精度水平相比，以前的模型的基础上直接，完全数值解的耦合通道薛定谔方程（CC）。在这里，从$^{7}$ Li $^{85}$ Rb的双光子光缔合光谱推导出的能级被分配通过应用MQDT方法，获得耦合通道问题的束缚态能量。我们的研究结果证实，MQDT产生一个紧凑的描述光缔合观测以及Fano-费什巴赫共振的位置和宽度。
Two-body loss rates for reactive collisions of cold atoms
本文提出了一个有效的双通道冷原子反应碰撞模型。它增加了具有不可逆的非弹性损失通道的弹性分子通道。散射研究与扭曲波玻恩近似，并产生角动量分辨截面以及两体损失率的一般表达式。显式表达式获得分段恒定电位。一个极点展开揭示了简单的通用形状函数的截面和两体损失率与维格纳阈值法律协议。这是适用于碰撞的亚稳态${^{20}}$ Ne -${^{21}}$ Ne原子，衰减主要通过放热潘宁，或缔合电离过程。从数值解的多通道薛定谔方程使用目前最好的分子势，我们得到了合成的散射数据。利用本文导出的二体损失形状函数，我们可以很好地匹配这些散射数据。
我们研究了超冷区的原子-离子散射。为了这个目的，一个分析模型的基础上的多通道量子亏损形式主义的发展和密切耦合的数值计算相比。我们研究的发生磁费什巴赫共振集中在特定的40 Ca + - Na系统。在实验上可达到的磁场中存在几种共振，应该可以精确地调节原子-离子相互作用。电荷交换过程的完全量子力学研究表明，即使存在共振效应，电荷交换速率也应该保持很小。我们的大部分结果都是与系统无关的，对于电荷中性超冷系统的实现具有重要意义。
We consider the coherent control of ultracold molecule-molecule scattering, impacted by a dense set of rovibrational resonances. To characterize the resonance spectrum, a rudimentary model based on multichannel quantum defect theory has been used to study the control of the scattering cross section and the reaction rate. Complete control around resonance energies is shown to be possible, but thermal averaging over a large number of resonances significantly reduces the extent of control of reaction rates due to the random distribution of optimal control parameters between resonances. We show th…
Precision measurements of transitions between singlet ($S=0$) Rydberg states of H$_2$ belonging to series converging on the $\mathrm{X}^+\,^2Σ_g^+(v^+=0,N^+=0)$ state of H$_2^+$ have been carried out by millimetre-wave spectroscopy under field-free conditions and in the presence of weak static electric fields. The Stark effect mixes states with different values of the orbital-angular-momentum quantum number $\ell$ and leads to quadratic Stark shifts of low-$\ell$ states and to linear Stark shifts of the nearly degenerate manifold of high-$\ell$ states. Transitions to the Stark manifold were ob…
Direct probe of anisotropy in atom-molecule collisions via quantum scattering resonances
各向异性是粒子相互作用的基本性质。它在冷和超冷分子过程中占据核心作用，其中已经发现长程力显著依赖于超冷极性分子碰撞中的取向。最近的实验表明，出现的量子现象，如散射共振在冷碰撞制度由于量子化的分子间的自由度。虽然这些状态已被证明是敏感的相互作用的细节，各向异性的量子共振的影响，迄今为止，逃避实验观察。在这里，我们通过改变分子内部转子的量子态，利用量子共振直接测量原子-分子相互作用的各向异性。我们观察到，只有当分子受到旋转激发时，分子氢与亚稳态氦的潘宁电离才会出现碰撞能量为$k_B$ x 270 mK的量子散射共振。我们使用最先进的从头算和多通道量子分子动力学计算表明，各向异性有助于有效的相互作用，只有$H_2$分子在第一激发旋转状态，而旋转基态$H_2$相互作用纯粹各向同性与亚稳态氦。控制内部分子旋转的量子态，使我们能够打开或关闭各向异性，从而解开相互作用的各向同性和各向异性部分。这些量子现象为最先进的理论描述提供了一个具有挑战性的基准，突出了使用冷碰撞来推进粒子相互作用的微观理解的优势。
We used the multichannel quantum defect theory to compute cross sections and rate coefficients for the dissociative recombination of CH$^+$ initially in its lowest vibrational level $v_i^+ = 0$ with electrons of incident energy bellow $0.2$ eV. We have focused on the contribution of the $2$ $^2Π$ state which is the main dissociative recombination route at low collision energies. The final cross section is obtained by averaging the relevant initial rotational states $(N_i^+ = 0,\dots,10)$ with a $300$ K Boltzmann distribution.The Maxwell isotropic rate coefficients for dissociative recombinatio…
We review the study of dissociative recombination and ro-vibrational excitation of diatomic and small polyatomic molecular ions initiating complex organic molecules formation. In particular, we show how Multichannel Quantum Defect Theory (MQDT) and R-matrix methods are used to compute cross sections and rate coefficients for cations in well defined ro-vibrational levels of the ground electronic state, from sub-meV up to few eV collision energies. The most recent MQDT results are compared with either other theoretical data, or with measured data obtained in storage-ring experiments.
We utilize two-photon high-precision microwave spectroscopy of $ng\rightarrow(n+2)g$ transitions to precisely measure the high-angular-momentum $g$-series quantum defect of $^{85}$Rb. Samples of cold Rydberg atoms in the $ng$ state are prepared via a three-photon optical excitation combined with controlled electric-field mixing and probed with 40-$μ$s-long microwave interaction pulses. The leading systematic uncertainty arises from DC Stark shifts, which is addressed by a cancellation of background electric fields in all three dimensions. From our measurements and an analysis of systematic unc…
We employ a quantum defect theory framework to provide a detailed analysis of the interplay between a magnetic Feshbach resonance and a shape resonance in cold collisions of ultracold $\rm ^{87}Rb$ atoms as captured in recent experiments using a laser-based collider [Phys. Rev. Research 3, 033209 (2021)]. By exerting control over a parameter space spanned by both collision energy and magnetic field, the width of a Feshbach resonance can be tuned over several orders of magnitude. We apply a quantum defect theory specialized for ultracold atomic collisions to fully describe of the experimental o…
