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arXiv:2004.11407 · Physical Review A

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

Kaitlin Moore, Alisher Duspayev, Ryan Cardman, Georg A. Raithel

Published Dec 22, 2020• 15 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.102.062817

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We utilize two-photon, high-precision microwave spectroscopy of ng\ensuremath→(n+2)gng\ensuremath{\rightarrow}(n+2)gng\ensuremath→(n+2)g transitions to precisely measure the high-angular-momentum ggg-series quantum defect of 85Rb^{85}\mathrm{Rb}85Rb. Samples of cold Rydberg atoms in the ngngng state are prepared via a three-photon optical excitation combined with controlled electric-field mixing and probed with 40-\ensuremathμs\ensuremath{\mu}\mathrm{s}\ensuremathμs-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 \ensuremathδ0=0.0039990(21){\ensuremath{\delta}}_{0}=0.003\phantom{\rule{0.16em}{0ex}}999\phantom{\rule{0.16em}{0ex}}0(21)\ensuremathδ0​=0.0039990(21) and \ensuremathδ2=\ensuremath−0.0202(21){\ensuremath{\delta}}_{2}=\ensuremath{-}0.0202(21)\ensuremathδ2​=\ensuremath−0.0202(21). We discuss our results in context with recent work elsewhere, as well as applications towards precision measurement.
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We report the measurement of the quantum defects of 85Rb P3/2 and F7/2-series Rydberg levels in a room temperature vapor cell by microwave-assisted electromagnetically induced transparency (EIT) spectroscopy. First, a novel microwave optical three-photon excitation method is employed to obtain the microwave-assisted EIT spectroscopy of the 5S1/2 − 5P3/2 – nD5/2 – (n+1)P3/2 or (n-1)F7/2 transition. Next, the Stark shifts of the corresponding Rydberg states relative to the Rabi frequency of microwave field are measured with high accuracy. Finally, the quantum defects, δ0 = 2.64142(15), δ2 = 0.295 for P3/2-series, and δ0 = 0.016411(16), δ2 = -0.0784 for F7/2-series, are forcibly extracted by the modified Rydberg-Ritz formula. This result can serve as a check on advanced theoretical calculations and promote the application of quantum simulations and quantum sensors in atomic ensembles.
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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 ${\ensuremath{\delta}}_{g}(n=30)=0.00405(6)$.
We use two-unequal-frequency microwave photons as sensitive probes to study the n s n s to the n p( n + m − 1)p Rydberg pair state transition in a cold 85 Rb gas, where n and m are integers. The principal quantum number n dependence of the energy differences between n s( n + 1)s and n p 3/2 n p 3/2 as well as n s( n + 2)s and n p 1/2 ( n + 1)p 1/2 has been measured and the results are consistent with the calculated values. Additionally, we demonstrate that the pair state Stark shift is the sum of the Stark shifts of both isolated Rydberg atoms. Finally, we tune the dipole–dipole mixing probability by applying an electric field to tune the energy difference between the dipole–dipole coupled states, n s( n + 2)s and n p 1/2 ( n + 1)p 1/2 . The results reported here are essential steps towards electric-field-controlled chemical reactions [1], quantum gates, molecular autoionization and few-body correlations.