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Physical Review A

High-resolution spectroscopy of Rydberg states in an ultracold cesium gas

Heiner Saßmannshausen, Frédéric Merkt, Johannes Deiglmayr

Published Mar 27, 2013• 53 citations
Publisher

Abstract

Transitions between high Rydberg states of ${}^{133}$Cs 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 $n=100$ 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 $nS$ and $nP$ Rydberg states of Cs beyond $n=90$. 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 $n$ values. The analysis also revealed that the initial polarization of the atomic sample ($F=4$, ${M}_{F}=4$) is preserved for several tens of microseconds, the depolarization being caused by slow precession along the magnetic stray fields.

DOI
10.1103/physreva.87.032519

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Physical Review A•May 13, 2003•307 citations
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 \ensuremathμ\ensuremath{\mu}\ensuremathμs. 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≈230n\ensuremath{\approx}230n\ensuremath≈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.
In highly excited Rydberg atoms, the excited electron is in a large, loosely bound orbit. Hence, in contrast with the ground states, the Rydberg states are very sensitive to external electric field and can be ionized in rather weak fields. The low ionization threshold of Rydberg states results in effective state-specific detection by the selective field ionization technique. \t In this thesis, high-resolution spectroscopy of Rydberg states of Rubidium using millimeter wave transitions and selective field ionization has been used as a probe of external electric and magnetic fields. Laser cooling and trapping techniques in a magneto-optical trap (MOT) are employed to have a high density and narrow velocity distribution for the atomic sample. In this work the magnetic field inhomogeneity inherent in a MOT is minimized and the stray electric field present at the trap region is compensated in order to have resolved spectra. The Stark line broadening of the spectra obtained in this work may be used to determine the electric field distribution in an expanding ultra-cold neutral plasma.
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 $30\text{\ensuremath{-}}\textmu{}\mathrm{s}$ 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 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 ${\overline{B}}_{\mathrm{HFS},{P}_{3/2}}=\ensuremath{-}0.084(102)$ 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.
I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii In highly excited Rydberg atoms, the excited electron is in a large, loosely bound orbit. Hence, in contrast with the ground states, the Rydberg states are very sensitive to external electric field and can be ionized in rather weak fields. The low ionization threshold of Rydberg states results in effective state-specific detection by the selective field ionization technique. In this thesis, high-resolution spectroscopy of Rydberg states of Rubidium using millimeter wave transitions and selective field ionization has been used as a probe of external electric and magnetic fields. Laser cooling and trapping techniques in a magneto-optical trap (MOT) are employed to have a high density and narrow velocity distribution for the atomic sample. In this work the magnetic field inhomogeneity inherent in a MOT is minimized and the stray electric field present at the trap region is compensated in order to have resolved spectra.
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.
We report on high-resolution microwave spectroscopy of cesium Rydberg $(n+2){D}_{5/2}\ensuremath{\rightarrow}n{F}_{J}$ transitions in a cold atomic gas. Atoms laser-cooled and trapped in a magnetic-optical trap are prepared in the DDD Rydberg state using a two-step laser excitation scheme. A microwave field transmitted into the chamber with a microwave horn drives the Rydberg transitions, which are probed via state selective field ionization. Varying duration and power of the microwave pulse, we observe Fourier sideband spectra as well as damped, on-resonant Rabi oscillations with pulse areas up to $\ensuremath{\gtrsim}3\ensuremath{\pi}$. Furthermore, we investigate the Zeeman effect of the clearly resolved nFJn{F}_{J}nFJ​ fine-structure levels in fields up to 120 mG, where the transition into nF7/2n{F}_{7/2}nF7/2​ displays a thee-peak Zeeman pattern, while nF5/2n{F}_{5/2}nF5/2​ shows a two-peak pattern. Our theoretical models explain all observed spectral characteristics, showing good agreement with the experiment. Our measurements provide a pathway for the study of high-angular-momentum Rydberg states, initialization and coherent manipulation of such states, Rydberg-atom macrodimers, and other Rydberg-atom interactions. Furthermore, the presented methods are suitable for calibration of microwave radiation as well as for nulling and calibration of dc magnetic fields in experimental chambers for cold atoms.
By using a magneto-optical trap we have measured the Rb $ns\ensuremath{-}(n+1)s$ and ${\mathrm{nd}}_{j}{\ensuremath{-}(n+1)d}_{j}$ two-photon millimeter-wave transitions for 32< n< 37,32<~n<~37,32< n< 37, observing 100-kHz-wide resonances, in spite of the trap's 10 G/cm magnetic-field gradient, in which one might expect to observe resonances 5 MHz wide. This resolution is possible because of the similarity of the gj{g}_{j}gj​ factors in the initial and final states. Under the same conditions, the single-photon ns-np resonances are \ensuremath{\sim}5 MHz wide. To make useful measurements of these intervals, we turned off the trap field and used the 300-K atoms of the background Rb vapor. Together these measurements improve the accuracy of the s, p, and d quantum defects by an order of magnitude.