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Physical Review A

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

Jeonghun Lee, Jirakan Nunkaew, Thomas F. Gallagher

Published Aug 10, 2016• 20 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.94.022505

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We present an experimental technique that allows us to determine the zero-field intervals between high-\ensuremathℓ\ensuremath{\ell}\ensuremathℓ 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≤n\ensuremath≤3027\ensuremath{\le}n\ensuremath{\le}3027\ensuremath≤n\ensuremath≤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 \ensuremathαd=9.12(2)a03{\ensuremath{\alpha}}_{d}=9.12(2){a}_{0}^{3}\ensuremathαd​=9.12(2)a03​ and \ensuremathαq=14(3)a05{\ensuremath{\alpha}}_{q}=14(3){a}_{0}^{5}\ensuremathαq​=14(3)a05​, 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.
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.
This paper reports on the results of experiments with cold rubidium Rydberg atoms in a magneto-optical trap. The specific feature of the experiments is the excitation of Rydberg atoms in a small volume within a cloud of cold atoms and the sorting of measured signals and spectra according to the number of detected Rydberg atoms. The effective lifetime of the 37 P Rydberg state and its polarizability in a weak electric field are measured. The results obtained are in good agreement with theoretical calculations. It is demonstrated that the localization of the excitation volume in the vicinity of the zero-magnetic-field point makes it possible to improve the spectral resolution and to obtain narrow microwave resonances in Rydberg atoms without switching off the quadrupole magnetic field of the trap. The dependence of the amplitude of dipole-dipole interaction resonances in Rydberg atoms on the number of atoms is measured. This dependence exhibits a linear behavior and agrees with the theory for a weak dipole-dipole interaction.
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 85Rb^{85}\mathrm{Rb}85Rb atoms from a magneto-optical trap were optically excited to 32d5∕232{d}_{5∕2}32d5∕2​ Rydberg states. The two-atom process $32{d}_{5∕2}+32{d}_{5∕2}\ensuremath{\rightarrow}34{p}_{3∕2}+30g$ is resonant at an electric field of approximately 0.3V∕cm0.3\phantom{\rule{0.3em}{0ex}}\mathrm{V}∕\mathrm{cm}0.3V∕cm. This process is driven by the electric dipole-dipole interaction, which is allowed due to the partial fff character that the ggg 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 85Rb^{85}\mathrm{Rb}85Rb ngngng-series quantum defect ${\ensuremath{\delta}}_{g}(n=30)=0.00405(6)$.
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.