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Results in Physics

Measurement of the quantum defects of 85Rb P and F-series via microwave-assisted electromagnetically induced transparency spectroscopy

Shaohua Li, Jinpeng Yuan, Lirong Wang, Liantuan Xiao, Suotang Jia

Published Aug 23, 2021• 12 citations
Publisher

Abstract

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.

DOI
10.1016/j.rinp.2021.104728

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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.
In this work, we precisely measure the transition energies between the Rydberg state n D 5 / 2 to the nearby Rydberg states ( n + 2 ) P 3 / 2 , ( n − 2 ) F 7 / 2 in 85 Rb for the range 41 ≤ n ≤ 46 . This was done by carrying out microwave spectroscopy via electromagnetically induced transparency (EIT) in a room temperature vapor reference cell of rubidium, which is similar to the experimental approach followed by Li et al., (2021). This range is interesting because there is a quasi Förster resonance between the atomic pair 43 D 5 / 2 + 43 D 5 / 2 and 45 P 3 / 2 + 41 F 7 / 2 . We compared the obtained results with numerically calculated transition energies based on previously tabulated quantum defect numbers by various research groups using both hot and ultra-cold atomic samples. Our data are more consistent with measurements made within ultra-cold atomic systems (Li et al., 2003; Han et al., 2006). • Precision Metrology. • Quantum Atomic Sensor. • Quantum Information Processing. • Quantum Computation. • Quantum Technologies.
In this work, we precisely measure the transition energies between the Rydberg state nD5/2\text{D}_{5/2}D5/2​ to the nearby Rydberg states $(\e{n}+2)\text{P}_{3/2}$, $(\e{n}-2)\text{F}_{7/2}$ for the range $41\leq \e{n}\leq46$. This was done by carrying out microwave spectroscopy via Electromagnetically Induced Transparency (EIT) in a room temperature vapor reference cell of Rubidium, which is similar to the experimental approach followed by Li et al. [Results in Physics \textbf{29}, 104728 (2021)]. This range is interesting because there is a quasi Förster resonance between the atomic pair 43D5/2+43D5/243\text{D}_{5/2}+43\text{D}_{5/2}43D5/2​+43D5/2​ and 45P3/2+41F7/245\text{P}_{3/2}+41\text{F}_{7/2}45P3/2​+41F7/2​. We compared the obtained results with numerically calculated transition energies based on previously tabulated quantum defect numbers by various research groups using both hot and ultra-cold atomic samples. Our data are more consistent with measurements made within ultra-cold atomic systems [Phys. Rev. A \textbf{67}, 052502 (2003), Phys. Rev. A \textbf{74}, 054502 (2006)].
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 demonstrate electromagnetically induced transparency (EIT) in a four-level cascade-like system, where the two upper levels are Rydberg states coupled by a microwave field. A two-photon transition consisting of an off-resonant microwave field and an off-resonant optical field forms an effective coupling field to induce transparency of the probe light. We characterize the Rabi frequency of the effective coupling field, as well as the EIT microwave spectra. The results show that microwave-assisted EIT allows us to efficiently access Rydberg states with relatively high orbital angular momentum ℓ=3, which is promising for the study of exotic Rydberg molecular states.
A comprehensive study of three-photon electromagnetically induced transparency (EIT) and absorption (EIA) on the rubidium cascade $5{S}_{1/2}\ensuremath{\rightarrow}5{P}_{3/2}$ (laser wavelength 780 nm), $5{P}_{3/2}\ensuremath{\rightarrow}5{D}_{5/2}$ (776 nm), and $5{D}_{5/2}\ensuremath{\rightarrow}28{F}_{7/2}$ (1260 nm) is performed. The 780-nm probe and 776-nm dressing beams are counteraligned through a Rb room-temperature vapor cell, and the 1260-nm coupler beam is co- or counteraligned with the probe beam. Several cases of EIT and EIA, measured over a range of detunings of the 776-nm beam, are studied. The observed phenomena are modeled by numerically solving the Lindblad equation, and the results are interpreted in terms of the probe-beam absorption behavior of velocity- and detuning-dependent dressed states. Interaction-time effects are discussed. To explore the utility of three-photon Rydberg EIA and EIT for microwave electric-field diagnostics, a sub-THz field generated by a signal source and a frequency quadrupler is applied to the Rb cell. The 100.633-GHz field resonantly drives the $28{F}_{7/2}\ensuremath{\leftrightarrow}29{D}_{5/2}$ transition and causes Autler-Townes splittings in the Rydberg EIA and EIT spectra, which are measured and employed to characterize the performance of the microwave quadrupler.