Rydberg Electrons as a Probe for Ultracold Systems

这个项目试图利用里德堡激发，将原子中的电子提升到非常高的能级，来探索超冷气体的新性质。超冷气体中的里德堡原子移动非常缓慢，导致碰撞时间很长，即使原子间作用力非常弱，也会产生巨大的累积效应。里德堡电子的大空间范围也使里德堡原子对局域场环境敏感。速度慢和空间体积大这两个因素的结合，使超冷里德堡原子成为研究超冷环境中微妙关联和其他新现象的理想探测器。在过去的几年里，在制备和操纵超冷里德堡原子方面的实验进展导致了原子、分子和光学(AMO)物理学的许多新的发展。例如，里德堡原子使探测一类新的远程分子，即所谓的类似三叶虫的分子，以及与量子信息革命相关的快速量子门成为可能。它们现在被用来使原本不透明的气体的小区域变得透明，使用的是众所周知的电磁诱导透明。里德堡原子还可以产生单光子源和调节光子-光子相互作用。因此，超冷里德堡原子研究架起了AMO、凝聚态和介观物理、量子信息科学以及超冷化学之间的桥梁。这一理论项目对里德堡电子与其环境的相互作用进行了建模，以更好地理解和预测观测到的光谱，这些光谱预计将敏感地取决于气体中原子的分布，并提高它们在上述区域的利用率。这项研究计划探索里德堡电子如何被用来研究少数和多体现象。里德堡电子为AMO、凝聚态物质和化学体系提供了低能量和良好局域化的探测器。虽然里德堡电子的波函数扩展到大体积，但在电离阈值附近被激发的里德堡电子具有很小的动能，对要研究的系统的扰动最小。里德堡电子可以从一个、两个或多个基态原子散射，这取决于邻近原子的密度。这些散射体对里德堡电子波函数的影响可以用来研究基态原子的性质，如它们的分布和关联，包括在简并的玻色或费米气体中。特别是，两个散射体的特殊情况可以揭示埃菲莫夫物理学，一个在核物理中引入的具有特殊性质的三体系统。为了进行这项研究，准确的波函数是当前方法难以提供的基本成分。在这里，将发展一种基于格林函数的非微扰方法来计算类里德堡三叶虫二聚体、三聚体等的波函数和势能面。这些精确的波函数将被用于光缔合(PA)谱的计算，其详细的线形将解锁关于基态原子的信息，包括它们的关联(来自二体、三体、四体或N体)。最后，结合Efimov波函数的计算，将有可能以光谱精度探测这些难以捉摸的状态。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This project seeks to utilize Rydberg excitations, promotion of an electron in an atom to a very high energy level, to probe novel properties of ultracold gases. Rydberg atoms within an ultracold gas move very slowly, resulting in long collision times and large cumulative effects of even very weak interatomic forces. The large spatial extent of the Rydberg electron also renders the Rydberg atom sensitive to local field environments. The combination of these two factors, slow speed and large spatial volume, makes ultracold Rydberg atoms ideal probes of delicate correlations and other novel phenomena within the ultracold environment. During the past few years, experimental progress in preparing and manipulating ultracold Rydberg atoms has led to many new developments in Atomic, Molecular, and Optical (AMO) Physics. For example, Rydberg atoms have made possible the detection of a new class of long-range molecules, the so-called "trilobite"-like molecules, and of fast quantum gates relevant to the quantum information revolution. They are now utilized to make small regions of an otherwise opaque gas transparent, using what is known as electromagnetically induced transparency. Rydberg atoms can also generate single photon sources and mediate photon-photon interactions. Accordingly, ultracold Rydberg atom research bridges AMO, condensed matter and mesoscopic physics, and quantum information science, as well as ultracold chemistry. This theory project models the interactions of Rydberg electrons with their environment in order to better understand and predict observed spectra, which are expected to depend sensitively on the distribution of atoms in the gas, and enhance their utilization in the range of areas mentioned above. This research program explores how Rydberg electrons can be used to investigate few- and many-body phenomena. Rydberg electrons provide a low-energy and well-localized probe for AMO, condensed-matter, and chemical systems. While their wave function extends to large volumes, Rydberg electrons, being excited near the ionization threshold, have a small kinetic energy that minimally perturbs a system to be investigated. Rydberg electrons can scatter from one, two, or many ground-state atoms depending on the density of neighboring atoms. The effect of those scatterers on the Rydberg electron wave function can be used to study the properties of the ground-state atoms, such as their distribution and correlation, including in degenerate Bose or Fermi gases. In particular, the special case of two scatterers can shed light on Efimov physics, a three-body system with peculiar properties introduced in nuclear physics. To carry out this research, accurate wave functions are essential ingredients that current methods struggle to provide. Here, a non-perturbative approach based on Green's functions to compute wave functions and potential energy surfaces for Rydberg trilobite-like dimers, trimers, etc., will be developed. These accurate wave functions will then be employed in the calculation of photo-association (PA) spectra whose detailed lineshapes will unlock the information about the ground-state atoms, including their correlation (from two, three, four, or N-body). Finally, together with the computation of the Efimov wave functions, the probing of those elusive states with spectroscopic accuracy will be made possible.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.