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Physical Review A

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

Jianing Han, Yasir Jamil, D.V.L. Norum, Paul J. Tanner, Thomas F. Gallagher

Published Nov 16, 2006• 128 citations
Publisher

Abstract

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 ${\mathrm{Rb}}^{+}$.

DOI
10.1103/physreva.74.054502

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Quantum Defect Measurements for High Angular Momentum Rydberg States of Potassium

Abraham Hill

We report measurements of the quantum defect for the f-, g-, and h-states of potassium with principal quantum number n between 26 and 29. Ground state potassium atoms in a magneto-optical trap are excited from the 4s state to the 5p state, then from the 5p state to the ndj state using lasers at 405nm and 980nm, respectively. We then measure the millimeter wave frequencies of the ndj to nl transitions. We extract the quantum defects from these frequency measurements in conjunction with the known d-state quantum defects. Experimental challenges with fully canceling the electric field and the inhomogeneity of the electric field inside the magneto-optical trap lead to our greatest sources of uncertainty. Our measurements show significant disagreement with predicted values that are calculated from the theoretical dipolar and quadrupolar polarizabilities of potassium.

•Jan 1, 2020•0 citations
Millimeter-wave resonance spectroscopy has been used to measure the (n+2)d5∕2(n+2){d}_{5∕2}(n+2)d5∕2​ to nf5∕2,7∕2n{f}_{5∕2,7∕2}nf5∕2,7∕2​ transition frequencies of cold 85Rb^{85}\mathrm{Rb}85Rb atoms in a magneto-optical trap. From these intervals we extract substantially improved Rb nfnfnf quantum defects, fine structure intervals, and limits for the dipole and quadrupole polarizabilities of Rb+{\mathrm{Rb}}^{+}Rb+.
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.
Millimeter resonances corresponding to single- and double-photon transitions have been observed between Rydberg levels of sodium with principal quantum number nnn 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.
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.
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)d5/2(n+1){d}_{5/2}(n+1)d5/2​ states to the ngngng and nhnhnh states of $27\ensuremath{\le}n\ensuremath{\le}30$. From the observed microwave transitions, we determine the quantum defects of the ngngng and nhnhnh states. Using the quantum defects of the ngngng and nhnhnh states and the adiabatic core polarization theory, we determine the Rb+{\mathrm{Rb}}^{+}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 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 measurements of the quantum defect for the f-, g-, and h-states of potassium with principal quantum number n between 26 and 29. Ground state potassium atoms in a magneto-optical trap are excited from the 4s state to the 5p state, then from the 5p state to the ndj state using lasers at 405nm and 980nm, respectively. We then measure the millimeter wave frequencies of the ndj to nl transitions. We extract the quantum defects from these frequency measurements in conjunction with the known d-state quantum defects. Experimental challenges with fully canceling the electric field and the inhomogeneity of the electric field inside the magneto-optical trap lead to our greatest sources of uncertainty. Our measurements show significant disagreement with predicted values that are calculated from the theoretical dipolar and quadrupolar polarizabilities of potassium.