arXiv:2304.07974 · Physical Review A

Quantum defects of n F J levels of Cs Rydberg atoms

Jingxu Bai, Rong Song, Jiabei Fan, Yuechun Jiao, Jianming Zhao, Suotang Jia, Georg A. Raithel

Published Aug 8, 2023• 13 citations

Abstract

We present precise measurements of the quantum defects of cesium $n{F}_{J}$ Rydberg levels. We employ high-precision microwave spectroscopy of $(n+2){D}_{5/2}\ensuremath{\rightarrow}n{F}_{5/2,7/2}$ transitions for $n=45$ to 50 in a cold-atom setup. Cold cesium $(n+2){D}_{5/2}$ atoms, prepared via two-photon laser excitation, are probed by scanning weak microwave fields interacting with the atoms across the $n{F}_{5/2,7/2}$ 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 $J=5/2$ and $7/2$, respectively. Fine-structure parameters ${A}_{\mathrm{FS}}$ and ${B}_{\mathrm{FS}}$ for Cs $n{F}_{J}$ are also obtained. Results are discussed in context with previous works, and the significance of the results is discussed.

DOI: 10.1103/physreva.108.022804

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Microwave spectroscopy and Zeeman effect of cesium ( n + 2 ) D 5 / 2 → n F J Rydberg transitions

Jingxu Bai, Rong Song, Xijun Li +4 more

arXiv:2309.04749Physical Review AFeb 27, 20246 citations

Measurement of the Rb g -series quantum defect using two-photon microwave spectroscopy

Kaitlin Moore, Alisher Duspayev, Ryan Cardman +1 more

arXiv:2004.11407Physical Review ADec 22, 202015 citations

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

Heiner Saßmannshausen, Frédéric Merkt, Johannes Deiglmayr

Physical Review AMar 27, 201353 citations

Millimeter spectroscopy in sodium Rydberg states: Quantum-defect, fine-structure, and polarizability measurements

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Measurement of the fine structure of cesium Rydberg state

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arXiv:2304.07974 · Physical Review A

Quantum defects of n F J levels of Cs Rydberg atoms

Jingxu Bai, Rong Song, Jiabei Fan, Yuechun Jiao, Jianming Zhao, Suotang Jia, Georg A. Raithel

Published Aug 8, 2023• 13 citations

arXiv HTML PDF

Abstract

We present precise measurements of the quantum defects of cesium

n{F}_{J}

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=45

to 50 in a cold-atom setup. Cold cesium

(n+2){D}_{5/2}

atoms, prepared via two-photon laser excitation, are probed by scanning weak microwave fields interacting with the atoms across the

n{F}_{5/2,7/2}

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=5/2

and

7/2

, respectively. Fine-structure parameters

{A}_{\mathrm{FS}}

and

{B}_{\mathrm{FS}}

for Cs

n{F}_{J}

are also obtained. Results are discussed in context with previous works, and the significance of the results is discussed.

DOI: 10.1103/physreva.108.022804

Related papers

Microwave spectroscopy and Zeeman effect of cesium ( n + 2 ) D 5 / 2 → n F J Rydberg transitions

Jingxu Bai, Rong Song, Xijun Li +4 more

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 $D$ 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 $n{F}_{J}$ fine-structure levels in fields up to 120 mG, where the transition into $n{F}_{7/2}$ displays a thee-peak Zeeman pattern, while $n{F}_{5/2}$ 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.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 $D$ 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 $n{F}_{J}$ fine-structure levels in fields up to 120 mG, where the transition into $n{F}_{7/2}$ displays a thee-peak Zeeman pattern, while $n{F}_{5/2}$ 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.

arXiv:2309.04749Physical Review AFeb 27, 20246 citations

Measurement of the Rb g -series quantum defect using two-photon microwave spectroscopy

Kaitlin Moore, Alisher Duspayev, Ryan Cardman +1 more

We utilize two-photon, high-precision microwave spectroscopy of $ng\ensuremath{\rightarrow}(n+2)g$ transitions to precisely measure the high-angular-momentum $g$ -series quantum defect of $^{85}\mathrm{Rb}$ . Samples of cold Rydberg atoms in the $ng$ state are prepared via a three-photon optical excitation combined with controlled electric-field mixing and probed with 40-$\ensuremath{\mu}\mathrm{s}$-long microwave interaction pulses. The leading systematic uncertainty arises from DC Stark shifts, which is addressed by a cancellation of background electric fields in all three dimensions. From our measurements and an analysis of systematic uncertainties from DC and AC Stark shifts, van der Waals interactions, and microwave frequency calibration, we obtain ${\ensuremath{\delta}}_{0}=0.003\phantom{\rule{0.16em}{0ex}}999\phantom{\rule{0.16em}{0ex}}0(21)$ and ${\ensuremath{\delta}}_{2}=\ensuremath{-}0.0202(21)$. We discuss our results in context with recent work elsewhere, as well as applications towards precision measurement.We utilize two-photon, high-precision microwave spectroscopy of $ng\ensuremath{\rightarrow}(n+2)g$ transitions to precisely measure the high-angular-momentum $g$-series quantum defect of $^{85}\mathrm{Rb}$. Samples of cold Rydberg atoms in the $ng$ state are prepared via a three-photon optical excitation combined with controlled electric-field mixing and probed with 40-$\ensuremath{\mu}\mathrm{s}$-long microwave interaction pulses. The leading systematic uncertainty arises from DC Stark shifts, which is addressed by a cancellation of background electric fields in all three dimensions. From our measurements and an analysis of systematic uncertainties from DC and AC Stark shifts, van der Waals interactions, and microwave frequency calibration, we obtain ${\ensuremath{\delta}}_{0}=0.003\phantom{\rule{0.16em}{0ex}}999\phantom{\rule{0.16em}{0ex}}0(21)$ and ${\ensuremath{\delta}}_{2}=\ensuremath{-}0.0202(21)$. We discuss our results in context with recent work elsewhere, as well as applications towards precision measurement.

arXiv:2004.11407Physical Review ADec 22, 202015 citations

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

Heiner Saßmannshausen, Frédéric Merkt, Johannes Deiglmayr

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.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.

Physical Review AMar 27, 201353 citations

Millimeter spectroscopy in sodium Rydberg states: Quantum-defect, fine-structure, and polarizability measurements

Claude Fabre, S. Haroche, P. Goy

Millimeter resonances corresponding to single- and double-photon transitions have been observed between Rydberg levels of sodium with principal quantum number $n$ ranging from 23 to 41. The levels are prepared by laser excitation; transitions are induced by microwaves produced by a backwave oscillator working around 300 GHz; detection is performed through the selective field-ionization technique. Experimental values for quantum defects, fine-structure intervals, and polarizabilities are reported.Millimeter resonances corresponding to single- and double-photon transitions have been observed between Rydberg levels of sodium with principal quantum number $n$ ranging from 23 to 41. The levels are prepared by laser excitation; transitions are induced by microwaves produced by a backwave oscillator working around 300 GHz; detection is performed through the selective field-ionization technique. Experimental values for quantum defects, fine-structure intervals, and polarizabilities are reported.

Physical Review AJul 1, 197876 citations

Measurement of the fine structure of cesium Rydberg state

Dong-Liang Pei, Jun He, Jieying Wang +2 more

The spectra of Rydberg atoms are of great significance for studying the energy levels of Rydberg atoms and the interaction between neutral atoms, especially, the high-precision spectra of Rydberg atoms can be used to measure the energy level shifts of Rydberg atoms resulting from the dipole-dipole interactions in room-temperature vapor cells. In this paper we report the preparation of cesium Rydberg states based on the cascaded two-photon excitation of 509 nm laser and 852 nm laser in opposite, and the measurements of the fine structure of cesium Rydberg states. In this experiment, the 509 nm laser is generated by the cavity-enhanced second-harmonic generation from 1018 nm laser with a periodically-poled KTP crystal and has a maximum power of about 1 W, and the 852 nm probe laser is provided by an external-cavity diode laser with a maximum output power of 5 mW and a typical linewidth of 1 MHz. By scanning the frequency of 509 nm coupling laser, it is presented that the Doppler-free spectra based on electromagnetically-induced transparency (EIT) of 509 nm coupling laser and 852 nm probe laser. The velocity-selective EIT spectra are used to study the spectral splitting of 6S1/26P3/257S(D) ladder-type system of cesium Rydberg atoms in a room-temperature vapor cell. The powers of 852 nm probe laser and 509 nm coupling laser are 0.3 upW and 200 mW, respectively. Their waist radii are both approximately 50 m. The intervals of hyperfine splitting of the intermediate state 6P3/2(F'=3, 4, 5) and fine splitting of 57D3/2 and 57D5/2 Rydberg states are measured by a frequency calibrating. Concretely, the velocity-selective spectrum with a radio frequency (RF) modulation of 30 MHz is used as a reference to calibrate the Rydberg fine-structure states in the hot vapor cell, where the RF frequency precision is smaller than a hertz on long time scales and the EIT linewidth is smaller than 13 MHz. The experimental value of the fine structure splitting of 57D3/2 and 57D5/2 Rydberg states is (354.72.5) MHz, that is in consistence with the value of 346.8 MHz calculated by Rydberg-Ritz equation and quantum defects of 57D3/2 and 57D5/2 Rydberg states. The experimental values of hyperfine splitting of intermediate state 6P3/2(F'=3, 4, 5) are also coincident with the theoretical calculated values. The dominant discrepancy existing between the experimental and calculated results may arise from the nonlinear correspondence of the PZT while the 509 nm wavelength cavity is scanned, and the measurement accuracy influenced by the spectral linewidth. The velocity-selective spectroscopy technique can also be used to measure the energy level shifts caused by the interactions of Rydberg atoms.The spectra of Rydberg atoms are of great significance for studying the energy levels of Rydberg atoms and the interaction between neutral atoms, especially, the high-precision spectra of Rydberg atoms can be used to measure the energy level shifts of Rydberg atoms resulting from the dipole-dipole interactions in room-temperature vapor cells. In this paper we report the preparation of cesium Rydberg states based on the cascaded two-photon excitation of 509 nm laser and 852 nm laser in opposite, and the measurements of the fine structure of cesium Rydberg states. In this experiment, the 509 nm laser is generated by the cavity-enhanced second-harmonic generation from 1018 nm laser with a periodically-poled KTP crystal and has a maximum power of about 1 W, and the 852 nm probe laser is provided by an external-cavity diode laser with a maximum output power of 5 mW and a typical linewidth of 1 MHz. By scanning the frequency of 509 nm coupling laser, it is presented that the Doppler-free spectra based on electromagnetically-induced transparency (EIT) of 509 nm coupling laser and 852 nm probe laser. The velocity-selective EIT spectra are used to study the spectral splitting of 6S1/26P3/257S(D) ladder-type system of cesium Rydberg atoms in a room-temperature vapor cell. The powers of 852 nm probe laser and 509 nm coupling laser are 0.3 upW and 200 mW, respectively. Their waist radii are both approximately 50 m. The intervals of hyperfine splitting of the intermediate state 6P3/2(F'=3, 4, 5) and fine splitting of 57D3/2 and 57D5/2 Rydberg states are measured by a frequency calibrating. Concretely, the velocity-selective spectrum with a radio frequency (RF) modulation of 30 MHz is used as a reference to calibrate the Rydberg fine-structure states in the hot vapor cell, where the RF frequency precision is smaller than a hertz on long time scales and the EIT linewidth is smaller than 13 MHz. The experimental value of the fine structure splitting of 57D3/2 and 57D5/2 Rydberg states is (354.72.5) MHz, that is in consistence with the value of 346.8 MHz calculated by Rydberg-Ritz equation and quantum defects of 57D3/2 and 57D5/2 Rydberg states. The experimental values of hyperfine splitting of intermediate state 6P3/2(F'=3, 4, 5) are also coincident with the theoretical calculated values. The dominant discrepancy existing between the experimental and calculated results may arise from the nonlinear correspondence of the PZT while the 509 nm wavelength cavity is scanned, and the measurement accuracy influenced by the spectral linewidth. The velocity-selective spectroscopy technique can also be used to measure the energy level shifts caused by the interactions of Rydberg atoms.

Acta Physica SinicaJan 1, 20176 citations

Microwave two-photon spectroscopy of cesium Rydberg atoms

Yongmei Xue, Yuechun Jiao, Liping Hao +1 more

We present a two-photon microwave spectra of cesium Rydberg atoms in the room-temperature vapor cell. The three-level atom including a ground state 6S1/2 (F = 4), an excited state 6P3/2 (F′ = 5) and Rydberg state consists of Rydberg electromagnetically induced transparency (Rydberg-EIT), that is employed to detect the microwave two-photon spectra. The microwave field with frequency ν DD = 11.42865 GHz couples the transition of Rydberg energy level |68D5/2〉 → |69D5/2〉, measured two-photon spectra display a rich of information including the microwave ac Stark shifts and two-photon Autler-Townes (AT) splitting. In the strong microwave field, the two-photon spectroscopy shows the state mixture between |68D5/2〉 and |68D3/2〉 Stark lines. The microwave two-photon spectra of the |69S1/2〉 → |70S1/2〉 transition coupled with frequency ν SS = 11.73503 GHz are also presented. The Floquet theory is employed to simulate the two-photon microwave spectra, showing the good agreement with the measurements. The work suggests the new method that may be used to investigate the multi-photon field-atom interaction and as an atom-based technique for precision field measurements.We present a two-photon microwave spectra of cesium Rydberg atoms in the room-temperature vapor cell. The three-level atom including a ground state 6S1/2 (F = 4), an excited state 6P3/2 (F′ = 5) and Rydberg state consists of Rydberg electromagnetically induced transparency (Rydberg-EIT), that is employed to detect the microwave two-photon spectra. The microwave field with frequency ν DD = 11.42865 GHz couples the transition of Rydberg energy level |68D5/2〉 → |69D5/2〉, measured two-photon spectra display a rich of information including the microwave ac Stark shifts and two-photon Autler-Townes (AT) splitting. In the strong microwave field, the two-photon spectroscopy shows the state mixture between |68D5/2〉 and |68D3/2〉 Stark lines. The microwave two-photon spectra of the |69S1/2〉 → |70S1/2〉 transition coupled with frequency ν SS = 11.73503 GHz are also presented. The Floquet theory is employed to simulate the two-photon microwave spectra, showing the good agreement with the measurements. The work suggests the new method that may be used to investigate the multi-photon field-atom interaction and as an atom-based technique for precision field measurements.

Optics ExpressDec 3, 20218 citations

We present precise measurements of the quantum defects of cesium

n{F}_{J}

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=45

to 50 in a cold-atom setup. Cold cesium

(n+2){D}_{5/2}

atoms, prepared via two-photon laser excitation, are probed by scanning weak microwave fields interacting with the atoms across the

n{F}_{5/2,7/2}

{\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=5/2

and

7/2

, respectively. Fine-structure parameters

{A}_{\mathrm{FS}}

and

{B}_{\mathrm{FS}}

for Cs

n{F}_{J}

are also obtained. Results are discussed in context with previous works, and the significance of the results is discussed.

D

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

n{F}_{J}

fine-structure levels in fields up to 120 mG, where the transition into

n{F}_{7/2}

displays a thee-peak Zeeman pattern, while

n{F}_{5/2}

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.

We utilize two-photon, high-precision microwave spectroscopy of $ng\ensuremath{\rightarrow}(n+2)g$ transitions to precisely measure the high-angular-momentum

g

-series quantum defect of

^{85}\mathrm{Rb}

. Samples of cold Rydberg atoms in the

ng

state are prepared via a three-photon optical excitation combined with controlled electric-field mixing and probed with 40-$\ensuremath{\mu}\mathrm{s}$-long microwave interaction pulses. The leading systematic uncertainty arises from DC Stark shifts, which is addressed by a cancellation of background electric fields in all three dimensions. From our measurements and an analysis of systematic uncertainties from DC and AC Stark shifts, van der Waals interactions, and microwave frequency calibration, we obtain ${\ensuremath{\delta}}_{0}=0.003\phantom{\rule{0.16em}{0ex}}999\phantom{\rule{0.16em}{0ex}}0(21)$ and ${\ensuremath{\delta}}_{2}=\ensuremath{-}0.0202(21)$. We discuss our results in context with recent work elsewhere, as well as applications towards precision measurement.

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.

Millimeter resonances corresponding to single- and double-photon transitions have been observed between Rydberg levels of sodium with principal quantum number

n

ranging from 23 to 41. The levels are prepared by laser excitation; transitions are induced by microwaves produced by a backwave oscillator working around 300 GHz; detection is performed through the selective field-ionization technique. Experimental values for quantum defects, fine-structure intervals, and polarizabilities are reported.