Physical Review A

Millimeter-wave spectroscopy of cold Rb Rydberg atoms in a magneto-optical trap: Quantum defects of the ns , np , and nd series

Wenhui Li, I. Mourachko, Michael W. Noel, Thomas F. Gallagher

Published May 13, 2003• 307 citations

Abstract

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 $32<~n<~37,$ 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 ${g}_{j}$ 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.

DOI: 10.1103/physreva.67.052502

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Rb nf quantum defects from millimeter-wave spectroscopy of cold Rb85 Rydberg atoms

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Physical Review ANov 16, 2006128 citations

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Microwave spectroscopy of the cold rubidium (n+1)d5/2→ng and nh transitions

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Physical Review AAug 10, 201620 citations

Physical Review A

Millimeter-wave spectroscopy of cold Rb Rydberg atoms in a magneto-optical trap: Quantum defects of the ns , np , and nd series

Wenhui Li, I. Mourachko, Michael W. Noel, Thomas F. Gallagher

Published May 13, 2003• 307 citations

Publisher

Abstract

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,

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

{g}_{j}

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.

DOI: 10.1103/physreva.67.052502

Related papers

Rb nf quantum defects from millimeter-wave spectroscopy of cold Rb85 Rydberg atoms

Jianing Han, Yasir Jamil, D.V.L. Norum +2 more

Millimeter-wave resonance spectroscopy has been used to measure the $(n+2){d}_{5∕2}$ to $n{f}_{5∕2,7∕2}$ transition frequencies of cold $^{85}\mathrm{Rb}$ atoms in a magneto-optical trap. From these intervals we extract substantially improved Rb $nf$ quantum defects, fine structure intervals, and limits for the dipole and quadrupole polarizabilities of ${\mathrm{Rb}}^{+}$ .Millimeter-wave resonance spectroscopy has been used to measure the $(n+2){d}_{5∕2}$ to $n{f}_{5∕2,7∕2}$ transition frequencies of cold $^{85}\mathrm{Rb}$ atoms in a magneto-optical trap. From these intervals we extract substantially improved Rb $nf$ quantum defects, fine structure intervals, and limits for the dipole and quadrupole polarizabilities of ${\mathrm{Rb}}^{+}$.

Physical Review ANov 16, 2006128 citations

Dipole-dipole broadening of Rb ns−np microwave transitions

Hyunwook Park, Paul J. Tanner, Brigitte J. C. Claessens +2 more

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Microwave Transitions of Cold Rydberg Atom Pairs

Jeonghun Lee

This dissertation consists of three microwave spectroscopy experiments performed with cold Rb Rydberg atoms in Magneto Optical Trap.The first experiment is a systematic study of a particular type of transition which was first observed in 2012 that involves a pair of Rydberg atoms.In this transition, even though only one microwave photon is absorbed, both atoms in the pair change states.In particular, we describe the transition with the configuration interaction (CI) model and experimentally verify the scaling of fractional population transfer predicted by the CI model.The second experiment builds on the first experiment and reports observations of additional single and multi photon microwave transitions that are allowed due to the same CI as in the first experiment.The observations show clearly that this type of transition involving a pair of Rydberg atoms are a lot more common than initially thought.We show that the transitions can be conveniently described as Forster resonances of Floquet states.The last experiment reports on the technique we used to measure the ng and nh series quantum defects and the ionic dipole and quadrupole polarizabilities of 85 Rb.The technique allows us to obtain zero field intervals of (n + 1)d 5/2 → ng and (n + 1)d 5/2 → nh intervals despite the fact that we can only control the stray electric field in one direction.Using the technique, the quantum defects of ng and nh were determined to be 0.0039741(16) and 0.0014066(57), respectively.The ionic II dipole and quadrupole polarizabilities were determined to be 9.12(2)a 3 0 and 14(3)a 5 0 , respectively.This dissertation consists of three microwave spectroscopy experiments performed with cold Rb Rydberg atoms in Magneto Optical Trap.The first experiment is a systematic study of a particular type of transition which was first observed in 2012 that involves a pair of Rydberg atoms.In this transition, even though only one microwave photon is absorbed, both atoms in the pair change states.In particular, we describe the transition with the configuration interaction (CI) model and experimentally verify the scaling of fractional population transfer predicted by the CI model.The second experiment builds on the first experiment and reports observations of additional single and multi photon microwave transitions that are allowed due to the same CI as in the first experiment.The observations show clearly that this type of transition involving a pair of Rydberg atoms are a lot more common than initially thought.We show that the transitions can be conveniently described as Forster resonances of Floquet states.The last experiment reports on the technique we used to measure the ng and nh series quantum defects and the ionic dipole and quadrupole polarizabilities of 85 Rb.The technique allows us to obtain zero field intervals of (n + 1)d 5/2 → ng and (n + 1)d 5/2 → nh intervals despite the fact that we can only control the stray electric field in one direction.Using the technique, the quantum defects of ng and nh were determined to be 0.0039741(16) and 0.0014066(57), respectively.The ionic II dipole and quadrupole polarizabilities were determined to be 9.12(2)a 3 0 and 14(3)a 5 0 , respectively.

Jul 13, 20170 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

Determination of the Rb ng-series quantum defect by resonant energy transfer spectroscopy of cold Rydberg atoms

K. Afrousheh, J. D. D. Martin, Joseph A. Petrus +1 more

Resonant energy transfer between cold Rydberg atoms was used to determine Rydberg atom energy levels, at precisions approaching those obtainable in microwave spectroscopy. Laser cooled Rb atoms from a magneto-optical trap were optically excited to 32d Rydberg states. The two-atom process 32d(j=5/2) + 32d(j=5/2) -> 34p(j=3/2) + 30g is resonant at an electric field of approximately 0.3 V/cm. This process is driven by the electric dipole-dipole interaction, which is allowed due to the partial f character that the g state acquires in an electric field. The experimentally observed resonant field, together with the Stark map calculation is used to make a determination of the Rb ng-series quantum defect: delta_g (n=30) = 0.00405(6).Resonant energy transfer between cold Rydberg atoms was used to determine Rydberg atom energy levels, at precisions approaching those obtainable in microwave spectroscopy. Laser cooled Rb atoms from a magneto-optical trap were optically excited to 32d Rydberg states. The two-atom process 32d(j=5/2) + 32d(j=5/2) -> 34p(j=3/2) + 30g is resonant at an electric field of approximately 0.3 V/cm. This process is driven by the electric dipole-dipole interaction, which is allowed due to the partial f character that the g state acquires in an electric field. The experimentally observed resonant field, together with the Stark map calculation is used to make a determination of the Rb ng-series quantum defect: delta_g (n=30) = 0.00405(6).

Aug 18, 20060 citations

Microwave spectroscopy of the cold rubidium (n+1)d5/2→ng and nh transitions

Jeonghun Lee, Jirakan Nunkaew, Thomas F. Gallagher

We present an experimental technique that allows us to determine the zero-field intervals between high-$\ensuremath{\ell}$ states of Rb in a magneto-optical trap, in spite of the fact that we can only control the stray electric field in one direction. The technique is based on measuring a property of the atom that depends on the field, as opposed to its square. This approach allows the determination of the zero-field intervals and the magnitude of the stray field in the uncontrolled perpendicular direction. We use this technique to observe the microwave transitions of rubidium from the $(n+1){d}_{5/2}$ states to the $ng$ and $nh$ states of $27\ensuremath{\le}n\ensuremath{\le}30$. From the observed microwave transitions, we determine the quantum defects of the $ng$ and $nh$ states. Using the quantum defects of the $ng$ and $nh$ states and the adiabatic core polarization theory, we determine the ${\mathrm{Rb}}^{+}$ ionic dipole and quadrupole polarizabilities to be ${\ensuremath{\alpha}}_{d}=9.12(2){a}_{0}^{3}$ and ${\ensuremath{\alpha}}_{q}=14(3){a}_{0}^{5}$, respectively.We present an experimental technique that allows us to determine the zero-field intervals between high-$\ensuremath{\ell}$ states of Rb in a magneto-optical trap, in spite of the fact that we can only control the stray electric field in one direction. The technique is based on measuring a property of the atom that depends on the field, as opposed to its square. This approach allows the determination of the zero-field intervals and the magnitude of the stray field in the uncontrolled perpendicular direction. We use this technique to observe the microwave transitions of rubidium from the $(n+1){d}_{5/2}$ states to the $ng$ and $nh$ states of $27\ensuremath{\le}n\ensuremath{\le}30$. From the observed microwave transitions, we determine the quantum defects of the $ng$ and $nh$ states. Using the quantum defects of the $ng$ and $nh$ states and the adiabatic core polarization theory, we determine the ${\mathrm{Rb}}^{+}$ ionic dipole and quadrupole polarizabilities to be ${\ensuremath{\alpha}}_{d}=9.12(2){a}_{0}^{3}$ and ${\ensuremath{\alpha}}_{q}=14(3){a}_{0}^{5}$, respectively.

Physical Review AAug 10, 201620 citations

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,

{g}_{j}

Millimeter-wave resonance spectroscopy has been used to measure the

(n+2){d}_{5∕2}

n{f}_{5∕2,7∕2}

transition frequencies of cold

^{85}\mathrm{Rb}

atoms in a magneto-optical trap. From these intervals we extract substantially improved Rb

nf

quantum defects, fine structure intervals, and limits for the dipole and quadrupole polarizabilities of

{\mathrm{Rb}}^{+}

{n}^{2}

, a broadening rate scaling as

{n}^{4}

is expected and a broadening rate of $8.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}{n}^{4}$ MHz cm

{}^{3}

is observed. The observed broadening is smaller than expected from a classical picture due to the spin-orbit interaction in the

np

atoms. The broadened resonances are asymmetric and cusp shaped, and their line shapes can be reproduced by a diatomic model which takes into account the dipole-dipole interaction, including the spin-orbit interaction, the strengths of the allowed microwave transitions, and the distribution of the atomic spacings in the trap.

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.

(n+1){d}_{5/2}

states to the

ng

and

nh

states of $27\ensuremath{\le}n\ensuremath{\le}30$. From the observed microwave transitions, we determine the quantum defects of the

ng

and

nh

states. Using the quantum defects of the

ng

and

nh

states and the adiabatic core polarization theory, we determine the

{\mathrm{Rb}}^{+}

ionic dipole and quadrupole polarizabilities to be ${\ensuremath{\alpha}}_{d}=9.12(2){a}_{0}^{3}$ and ${\ensuremath{\alpha}}_{q}=14(3){a}_{0}^{5}$, respectively.