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arXiv:2507.08278 · Proceedings of the National Academy of Sciences

Observation of the electric Breit–Rabi effect

S.-Z. Wang, Shou-Bo Wang, Zhi-Jin Tao, Tian Xia, Zheng‐Tian Lu

Published Jun 27, 2025• 0 citations
arXivHTMLPDF

Abstract

The response of an atom to external electric and magnetic fields can reveal fundamental atomic properties. It has long been verified that, in a static magnetic field, those atomic energy levels with hyperfine interactions shift according to the Breit-Rabi formula, which introduces nonlinear dependence on the magnetic field. On the other hand, the corresponding Breit-Rabi dependence on a static electric field has not been observed before due to a combination of experimental challenges. Here, we precisely measure the Stark shift of the [Formula: see text] transition of [Formula: see text]Yb ([Formula: see text] = 1/2) with cold atoms held by an optical dipole trap in a static electric field up to 120 kV/cm. We observe the electric Breit-Rabi effect displaying high-order ([Formula: see text] and [Formula: see text]) DC Stark shifts. These effects arise from the influence of the strong electric field on hyperfine interactions.

DOI
10.1073/pnas.2423902122

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The response of an atom to external electric and magnetic fields can reveal fundamental atomic properties. It has long been verified that, in a static magnetic field, those atomic energy levels with hyperfine interactions shift according to the Breit-Rabi formula, which introduces nonlinear dependence on the magnetic field. On the other hand, the corresponding Breit-Rabi dependence on a static electric field has not been observed before due to a combination of experimental challenges. Here, we precisely measure the Stark shift of the [Formula: see text] transition of [Formula: see text]Yb ([Formula: see text] = 1/2) with cold atoms held by an optical dipole trap in a static electric field up to 120 kV/cm. We observe the electric Breit-Rabi effect displaying high-order ([Formula: see text] and [Formula: see text]) DC Stark shifts. These effects arise from the influence of the strong electric field on hyperfine interactions.
In this work, numerical calculations were implemented based on the diagonalisation of a matrix representation of the Stark Hamiltonian on a subset of the basis given by the zero-field Hamiltonian. Dipole matrix elements between the involved states were calculated, which allow for the prediction of transition strengths to Stark shifted Rydberg states. The applicability of the numerical methods were confirmed experimentally by precision spectroscopy in a rubidium vapour cell with electrodes using electromagnetically induced transparency (EIT). The numerical methods were then extended to predict ionisation rates of Rydberg states in the highly Stark shifted regime beyond the classical ionisation threshold. For this purpose, a complex absorbing potential (CAP) was specifically adjusted to the Stark Hamiltonian. An experiment was conducted, in which cold atoms from a magneto-optical trap (MOT) were excited to Stark shifted Rydberg states and the arising ions were detected. The obtained ionisation spectra agree well with the results from the numerical calculations. Another extension of the numerical methods was implemented for crossed electric and magnetic fields. This was used for approximate calculations of the motional Stark effect (MSE), which acts on atoms moving through static magnetic fields and thereby experiencing a Lorentz electric field. In a precision spectroscopy, once more using EIT in a vapour cell, the MSE was observed in low magnetic fields for the first time in rubidium. The spectral shift, which is caused by the MSE, matches the prediction from the numerical calculations. In a final experiment, the practical use of the knowledge of several properties of Stark shifted Rydberg states was illustrated. The numerical methods including the CAP were used to specifically select states for their optical accessibility, permanent electric dipole moments and ionisation rates. In the experiment, atoms from a MOT were excited to these states to observe different characteristics of the dipole blockade effect. The detection scheme for this experiment was realised by controlled ionisation using only small changes in the external electric field.
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We have measured the magnetic dipole (M1) and electric quadrupole (E2) amplitudes in the D1 transition of rubidium atoms placed in a static electric field, ${\mathit{scrE}\ensuremath{\rightarrow}}_{\mathit{s}}$. The interference of the Stark induced M1 and E2 amplitudes with the normal E1 amplitude gives the atomic absorptivity a linear dependence on ${\mathit{scrE}\ensuremath{\rightarrow}}_{\mathit{s}}$ and on the atomic spin polarization. We find that the fractional change in absorptivity due to the Stark interference is aM1{\mathit{a}}_{\mathit{M}1}aM1​+aE2{\mathit{a}}_{\mathit{E}2}aE2​=(-2.37\ifmmode\pm\else\textpm\fi{}0.37\ifmmode\pm\else\textpm\fi{}0.28)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}8}$ (kV/cm${)}^{\mathrm{\ensuremath{-}}1}$.
Effects of static electric and magnetic fields on the differential ac Stark shifts for microwave transitions in ultracold bosonic 87{}^{87}87Rb133{}^{133}133Cs molecules are studied experimentally. The ac Stark effect is greatly simplified by applying a dc electric field in addition to the magnetic field.
Obtaining an accurate value of the electric dipole moment μ is essential in the fields of laser application technologies. A direct way of measuring the electric dipole moment μ is to observe the Rabi-oscillation which manifests itself in the coherent photo-excitation behavior of atoms. In the case of the elements which have large angular momenta, identifying the Rabi-oscillation in their excitation behavior becomes rather difficult. We proposed an accurate and straightforward method of determining the electric-dipole moment μ between multifold degenerate levels. The point is to remove the degeneracy by applying an external magnetic field with the aid of the Zeeman effect and, then, to realize a degeneration free coherent excitation. As a result, we can observe the Rabi-oscillations explicitly in the excitation vs. laser-fluence curves. The present method provides a reliable basis of experimental determination of μ. As an example, we applied the present method to a transition to 0–17,362 cm−1 level in uranium and obtained the value μ=0.86±0.06 (Debye).
We experimentally show that an electric dipole moment of more than 1 Debye can be induced in the dysprosium (Dy) atom, in a long-lived state that is about 17 513 cm − 1 above the ground state. This metastable state is part of a strongly coupled opposite-parity doublet. Using optically detected microwave spectroscopy in an atomic beam, we determine the approximately 1.12 cm − 1 doublet spacing for the five stable bosonic isotopes of Dy with kilohertz-level accuracy. From the shift of the microwave transition frequency in low electric fields (below 150 V/cm) and from optical spectra in high electric fields (up to 150 kV/cm), a reduced transition dipole moment of 7.65 ± 0.05 Debye between the doublet states is extracted. In high electric fields the doublet interacts with a third state at 17 727 cm − 1 that connects to the ground state via an electric-dipole transition. The three-state Stark interaction enables preparation of Dy atoms in the metastable state via single-photon excitation from the ground state. Our work experimentally validates predicted characteristics of the opposite-parity doublet and provides an effective route to the first doubly polar quantum gas of atoms.