Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · physics/0010038

Resummation of the Divergent Perturbation Series for a Hydrogen Atom in an Electric Field

U. D. Jentschura
View original source ↗Read source document ↗Export metadata ↓

Abstract

We consider the resummation of the perturbation series describing the energy displacement of a hydrogenic bound state in an electric field (known as the Stark effect or the LoSurdo-Stark effect), which constitutes a divergent formal power series in the electric field strength. The perturbation series exhibits a rich singularity structure in the Borel plane. Resummation methods are presented which appear to lead to consistent results even in problematic cases where isolated singularities or branch cuts are present on the positive and negative real axis in the Borel plane. Two resummation prescriptions are compared: (i) a variant of the Borel-Pade resummation method, with an additional improvement due to utilization of the leading renormalon poles (for a comprehensive discussion of renormalons see [M. Beneke, Phys. Rep. vol. 317, p. 1 (1999)]), and (ii) a contour-improved combination of the Borel method with an analytic continuation by conformal mapping, and Pade approximations in the conformal variable. The singularity structure in the case of the LoSurdo-Stark effect in the complex Borel plane is shown to be similar to (divergent) perturbative expansions in quantum chromodynamics.

Explore related subjects

physics.atom-phhep-phquant-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

U. D. Jentschura. 2001-04-23. Resummation of the Divergent Perturbation Series for a Hydrogen Atom in an Electric Field. https://doi.org/10.1103/physreva.64.013403

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Vector Measurements Using Integrated Radio Frequency Atomic Magnetometers

We demonstrate reconstruction of three-dimensional radio-frequency (RF) magnetic-field vectors using a pair of integrated RF atomic magnetometers operated with orthogonal bias-field orientations. A theoretical and experimental analysis identifies a phase-ambiguity dead band that limits reconstruction when the two sensor responses become nearly identical. Measurements performed in an unshielded laboratory environment demonstrate accurate reconstruction of RF magnetic-field orientations and validate the predicted dependence of reconstruction accuracy on signal imbalance. These results establish integrated RF atomic magnetometers as a compact and sensitive platform for directional RF magnetic-field sensing, particularly at low frequencies, and provide a foundation for portable source-localization and field-mapping applications.

physics.atom-ph↗
arXiv2026

Anomalously enhanced lifetimes of low angular momentum Rydberg states in singly charged alkaline-earth metal ions

Trapped ions excited to high-lying electronic states, so-called Rydberg states, open new opportunities for quantum simulation and quantum computing. Generally, the fidelity of quantum coherent operations critically depends on the longevity of Rydberg states. However, scaling laws predict that the lifetimes of Rydberg states in singly charged alkaline-earth metal ions are 16 times shorter, compared to their neutral atom counterparts. Here, we show that this is not generally the case. We report an anomalous lifetime enhancement of certain low angular momentum ionic Rydberg series by factors larger than eight. The anomaly is present at both zero and finite temperature, although it is caused by different mechanisms. At zero temperature, the anomalously enhanced lifetimes are caused by accidental cancellations of the relevant dipole transition matrix elements, while at room temperature the anomaly originates from the enlarged energetic separation of ionic Rydberg levels with respect to neutral-atom levels.

physics.atom-ph↗
arXiv2026

Ytterbium lattice clock with systematic uncertainty of $1.3\times 10^{-18}$ and instability at the $10^{-19}$ level

We report an optical lattice clock based on $^{171}$Yb atoms with a total systematic uncertainty of $1.3\times 10^{-18}$. An in-vacuum buildup cavity was employed to enhance the lattice light power. Differential frequency measurement between two identical clocks facilitates the evaluation of systematic shifts. Synchronous comparison of the two clocks reached a stability level of $2.7\times 10^{-19}$ in an averaging time of 216,000~s. The blackbody radiation (BBR) shield which is placed in vacuum provides a well-characterized BBR environment, enabling an uncertainty contribution of $8.7\times 10^{-19}$ from the BBR Stark shift. Lattice light shifts were measured at different lattice depths $U$, and fitted with a fourth-order polynomial of $U$. The zero-linear-shift frequency $ν_{\mathrm{zero}}$ was determined to be 394 798 260.6(3) MHz. The lattice light shift can be controlled at an uncertainty level of $6.3\times 10^{-19}$ under typical operating conditions. Other systematic shifts have also been evaluated. The two clocks will be used for remote frequency comparisons between Shanghai and Wuhan.

physics.atom-ph↗