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Chinese Physics B

Pure hyperfine spectra of KRb in its vibronic ground state: Towards the determination of nuclear spin–spin interaction

Qi Ouyang, Xuping Shao, Huang Yun-Xia, Xiaohua Yang

Published Mar 7, 2025• 1 citation

Abstract

Abstract The Zeeman-hyperfine-rotational spectra of 40K87Rb within its vibronic ground state at a magnetic field of 545.9 G are investigated by adopting the latest molecular constants available, and the results are in good agreement with the experimental observation made by Ospelkaus et al. [Phys. Rev. Lett. 104 030402 (2010)]. However, the calculated spectra generally shift by −3.6 kHz from the experimental ones, which implies the inaccuracy of the effective rotational constant. Therefore, we refit the spectra and obtain a new B eff = 1113952(1) kHz, which reduces the overall root-mean-square deviation from 10.8 kHz to 7.9 kHz. Furthermore, the pure hyperfine spectra within the J = 0 and 1 rotational states are simulated. We find that the scalar nuclear spin–spin interaction dominates the hyperfine splitting of J = 0 despite it being slightly indirectly affected by the nuclear electric quadruple interaction due to the rotational perturbation, while the nuclear electric quadrupole interactions dominate the splitting, and the scalar and tensor nuclear spin–spin interactions also affect the splitting of J = 1. The detailed hyperfine-rotational perturbations are studied. Therefore, the scalar and tensor nuclear spin–spin interaction constants can be precisely determined by simultaneously measuring the pure hyperfine radio-frequency spectra of the J = 0 and 1 states in the vibronic ground state.

DOI: 10.1088/1674-1056/adbdc1

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Abstract The Zeeman-hyperfine-rotational spectra of 40K87Rb within its vibronic ground state at a magnetic field of 545.9 G are investigated by adopting the latest molecular constants available, and the results are in good agreement with the experimental observation made by Ospelkaus et al. [Phys. Rev. Lett. 104 030402 (2010)]. However, the calculated spectra generally shift by −3.6 kHz from the experimental ones, which implies the inaccuracy of the effective rotational constant. Therefore, we refit the spectra and obtain a new B eff = 1113952(1) kHz, which reduces the overall root-mean-square deviation from 10.8 kHz to 7.9 kHz. Furthermore, the pure hyperfine spectra within the J = 0 and 1 rotational states are simulated. We find that the scalar nuclear spin–spin interaction dominates the hyperfine splitting of J = 0 despite it being slightly indirectly affected by the nuclear electric quadruple interaction due to the rotational perturbation, while the nuclear electric quadrupole interactions dominate the splitting, and the scalar and tensor nuclear spin–spin interactions also affect the splitting of J = 1. The detailed hyperfine-rotational perturbations are studied. Therefore, the scalar and tensor nuclear spin–spin interaction constants can be precisely determined by simultaneously measuring the pure hyperfine radio-frequency spectra of the J = 0 and 1 states in the vibronic ground state.

We investigate the hyperfine energy levels and Zeeman splittings for homonuclear alkali-metal dimers in low-lying rotational and vibrational states, which are important for experiments designed to produce quantum gases of deeply bound molecules. We carry out density-functional theory calculations of the nuclear hyperfine coupling constants. For nonrotating states, the zero-field splittings are determined almost entirely by the scalar nuclear spin-spin coupling constant. By contrast with the heteronuclear case, the total nuclear spin remains a good quantum number in a magnetic field. We also investigate levels with rotational quantum number

N=1

, which have long-range anisotropic quadrupole-quadrupole interactions and may be collisionally stable. For these states the splitting is dominated by nuclear quadrupole coupling for most of the alkali-metal dimers and the Zeeman splittings are considerably more complicated.

We investigate the energy levels of heteronuclear alkali-metal dimers in levels correlating with the lowest rotational level of the ground electronic state, which are important in efforts to produce ground-state ultracold molecules. We use density-functional theory to calculate nuclear quadrupole and magnetic coupling constants for KRb and RbCs and explore the hyperfine structure in the presence of electric and magnetic fields. For nonrotating states, the zero-field splittings are dominated by the electron-mediated part of the nuclear spin-spin coupling. They are a few kilohertz for KRb isotopologs and a few tens of kilohertz for RbCs isotopologs.

Among the possible types of magnetic dipole interactions in molecular systems, couplings between nuclear motion and the nuclear spin have probably received the least attention in molecular spectroscopy. Although very small in comparison to effects related to electron spin, this type of hyperfine interaction plays an important role in the NMR spectroscopy of molecular systems. While measurement and prediction of spin-rotation tensors are a common place, vibrationally induced effects still lack a comprehensive description. In this article we develop a generic, theoretical framework that is well embedded in modern electronic structure theory and inspired by the Breit-Pauli Hamiltonian for electronic interactions, distinguishing between nuclear spin-orbit and spin-other-orbit contributions. We show that the interaction of nuclear spins with pseudorotational excitations of highly symmetric molecules may lead to experimentally accessible hyperfine splittings in NMR spectra, triggered by infrared light.

We report microwave spectroscopy of

^{167}

Er

^{3+}

doped in CaWO

_4

which reveals the hyperfine splitting of the erbium electronic ground state (

Z_1

,

J_\mathrm{eff.}

=15/2) induced by the

I

=7/2 nuclear spin. From spectra measured below$\sim$50 mK in magnetic fields up to 200 mT, we extract spin Hamiltonian parameters including the electron

\textbf{g}

, hyperfine

\textbf{A}

, and nuclear electric quadrupolar

\textbf{Q}

tensors. Crucially, our analysis demonstrate unambiguously, that the previously unobserved nuclear electric quadrupolar moment is essential to reproduce the experimental data. With these refined parameters, we identify zero first-order Zeeman (ZEFOZ) transitions at zero magnetic field. Extending the analysis to finite fields, we uncover that ZEFOZ points lie either along the

c

axis or within the

a

-

b

plane. These results establish CaWO

_4

as a promising host for long lifetime quantum memories.