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arXiv:2410.09520 · Physical Review A

Measurements of the hyperfine structure of n P J Rydberg states by microwave spectroscopy in Cs atoms

Rong Song, Jingxu Bai, Zhenhua Li, Yuechun Jiao, Suotang Jia, Jianming Zhao

Published Oct 11, 2024• 3 citations
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Abstract

We present measurements of the hyperfine structure (HFS) of the $n{P}_{J}$ Rydberg states for a large range of principal quantum number $n$ $(n=41--55)$ employing microwave spectroscopy in an ultracold cesium Rydberg ensemble. A microwave field with $30\text{\ensuremath{-}}\textmu{}\mathrm{s}$ duration couples the $nS\ensuremath{\rightarrow}nP$ transition, yielding a narrow linewidth spectroscopy that approaches the Fourier limit, which allows us to resolve the hyperfine structure of $n{P}_{J}$ states. By analyzing the hyperfine splittings of $n{P}_{J}$ states, we determine the magnetic dipole HFS coupling constant ${\overline{A}}_{\mathrm{HFS},{P}_{1/2}}=3.760(26)$ GHz for the ${P}_{1/2}$ state, and ${\overline{A}}_{\mathrm{HFS},{P}_{3/2}}=0.718(27)$ GHz and ${\overline{B}}_{\mathrm{HFS},{P}_{3/2}}=\ensuremath{-}0.084(102)$ GHz for the ${P}_{3/2}$ state. Systematic uncertainties caused by stray electromagnetic field, microwave field power, and Rydberg interaction are analyzed. This measurement is significant for the investigation of Rydberg electrometry and quantum simulation with dipole interaction involving the $n{P}_{J}$ state.

DOI
10.1103/physreva.110.042815

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We present measurements of the hyperfine structure (HFS) of the nPJn{P}_{J}nPJ​ Rydberg states for a large range of principal quantum number nnn (n=41−−55)(n=41--55)(n=41−−55) employing microwave spectroscopy in an ultracold cesium Rydberg ensemble. A microwave field with 30\ensuremath-\textmus30\text{\ensuremath{-}}\textmu{}\mathrm{s}30\ensuremath-\textmus duration couples the nS\ensuremath→nPnS\ensuremath{\rightarrow}nPnS\ensuremath→nP transition, yielding a narrow linewidth spectroscopy that approaches the Fourier limit, which allows us to resolve the hyperfine structure of nPJn{P}_{J}nPJ​ states. By analyzing the hyperfine splittings of nPJn{P}_{J}nPJ​ states, we determine the magnetic dipole HFS coupling constant A‾HFS,P1/2=3.760(26){\overline{A}}_{\mathrm{HFS},{P}_{1/2}}=3.760(26)AHFS,P1/2​​=3.760(26) GHz for the P1/2{P}_{1/2}P1/2​ state, and A‾HFS,P3/2=0.718(27){\overline{A}}_{\mathrm{HFS},{P}_{3/2}}=0.718(27)AHFS,P3/2​​=0.718(27) GHz and B‾HFS,P3/2=\ensuremath−0.084(102){\overline{B}}_{\mathrm{HFS},{P}_{3/2}}=\ensuremath{-}0.084(102)BHFS,P3/2​​=\ensuremath−0.084(102) GHz for the P3/2{P}_{3/2}P3/2​ state. Systematic uncertainties caused by stray electromagnetic field, microwave field power, and Rydberg interaction are analyzed. This measurement is significant for the investigation of Rydberg electrometry and quantum simulation with dipole interaction involving the nPJn{P}_{J}nPJ​ state.
We measure the hyperfine structure of nP1/2n{P}_{1/2}nP1/2​ Rydberg states for n=n=n= 42, 43, 44, and 46 using mm-wave spectroscopy on an ensemble of laser-cooled 85Rb^{85}\mathrm{Rb}85Rb atoms. Systematic uncertainties in our measurement from the Zeeman splittings induced by stray magnetic fields and dipole-dipole interactions between two Rydberg atoms are factored in with the obtained statistical uncertainty. Our final measurement of the nP1/2n{P}_{1/2}nP1/2​ hyperfine coupling constant is AHFS=1.443(31){A}_{\text{HFS}}=1.443(31)AHFS​=1.443(31) GHz. This measurement is useful for studies of long-range Rydberg molecules, Rydberg electrometry, and quantum simulation with dipole-dipole interactions involving nP1/2n{P}_{1/2}nP1/2​ atoms.
We perform measurements of microwave spectra of cesium Rydberg 51 S 1/2 → 51 P J transitions with the linewidth approaching the Fourier limit. A two-photon scheme excites the ground-state atoms to the Rydberg 51 S 1/2 state, and a weak microwave photon couples the Rydberg transition of 51 S 1/2 → 51 P J . The hyperfine structure of 51 P 1/2 can be clearly resolved with a narrow linewidth microwave spectra by using the method of ion detection. Furthermore, we investigate the Zeeman effect of the 51 P 1/2,3/2 state. The theoretical calculations reproduce the measurement well. Our experimental measurements provide a reliable technical solution for the investigation of high angular momentum Rydberg states, which is conducive to further realizing the coherent manipulation of Rydberg energy levels and improving the sensitivity of electromagnetic field measurement.
Transitions between high Rydberg states of 133{}^{133}133Cs atoms have been studied by high-resolution millimeter-wave spectroscopy of an ultracold sample. The spectroscopic measurements were performed after releasing the atoms from a magneto-optical trap. Switching off all trapping fields and compensating the stray electric and magnetic fields to below 1 mV/cm and 2 mG, respectively, prior to the spectroscopic measurement enabled the recording of millimeter-wave spectra of Rydberg states with principal quantum number beyond n=100n=100n=100 under conditions where the inhomogeneous broadening by stray fields is minimal and no dephasing of the Rydberg-atom sample can be detected over measurement times up to 60 $\ensuremath{\mu}$s. The Fourier-transform-limited line widths of better than 20 kHz enabled the observation of the hyperfine structure of nSnSnS and nPnPnP Rydberg states of Cs beyond n=90n=90n=90. The analysis of the line shapes of transitions to Rydberg states with $n\ensuremath{\approx}230$ indicated that field inhomogeneities across the atomic sample represent the dominant cause of spectral broadening at high nnn values. The analysis also revealed that the initial polarization of the atomic sample (F=4F=4F=4, MF=4{M}_{F}=4MF​=4) is preserved for several tens of microseconds, the depolarization being caused by slow precession along the magnetic stray fields.
We present measurements of the hyperfine structure splittings of nS1/2n{S}_{1/2}nS1/2​ Rydberg states of 85Rb^{85}\mathrm{Rb}85Rb for n=43n=43n=43, 44, 45, and 46. From the splittings, the hyperfine coupling constant, AHFS{A}_{\mathrm{HFS}}AHFS​, is determined to be 15.372(80) GHz. This result is an order-of-magnitude improvement from previous measurements. We study and account for systematic uncertainty sources, such as unwanted electric and magnetic fields, dipolar Rydberg-Rydberg interactions, and ac shifts. Initial evidence for hyperfine-mixed Rydberg pair states is found.
We present precise measurements of the quantum defects of cesium nFJn{F}_{J}nFJ​ Rydberg levels. We employ high-precision microwave spectroscopy of $(n+2){D}_{5/2}\ensuremath{\rightarrow}n{F}_{5/2,7/2}$ transitions for n=45n=45n=45 to 50 in a cold-atom setup. Cold cesium (n+2)D5/2(n+2){D}_{5/2}(n+2)D5/2​ atoms, prepared via two-photon laser excitation, are probed by scanning weak microwave fields interacting with the atoms across the nF5/2,7/2n{F}_{5/2,7/2}nF5/2,7/2​ resonances. Transition spectra are acquired using state-selective electric-field ionization and time-gated ion detection. Transition-frequency intervals are obtained by Lorentzian fits to the measured spectral lines, which have linewidths ranging between 70 and 190 kHz, corresponding to about one to three times the Fourier limit. A comprehensive analysis of relevant line-shift uncertainties and line-broadening effects is conducted. We find quantum defect parameters ${\ensuremath{\delta}}_{0}({F}_{5/2})=0.033\phantom{\rule{0.16em}{0ex}}415\phantom{\rule{0.16em}{0ex}}37(70)$ and ${\ensuremath{\delta}}_{2}({F}_{5/2})=\ensuremath{-}0.2014(16)$, as well as ${\ensuremath{\delta}}_{0}({F}_{7/2})=0.033\phantom{\rule{0.16em}{0ex}}564\phantom{\rule{0.16em}{0ex}}6(13)$ and ${\ensuremath{\delta}}_{2}({F}_{7/2})=\ensuremath{-}0.2052(29)$, for J=5/2J=5/2J=5/2 and 7/27/27/2, respectively. Fine-structure parameters AFS{A}_{\mathrm{FS}}AFS​ and BFS{B}_{\mathrm{FS}}BFS​ for Cs nFJn{F}_{J}nFJ​ are also obtained. Results are discussed in context with previous works, and the significance of the results is discussed.
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