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Photonics

Microwave-Controlled Spectroscopy Evolution for Different Rydberg States

Yinglong Diao, Haoliang Hu, Xiaofei Li, Zhibo Li, Feitong Zeng, Yanbin Chen, Shuhang You

Published Jul 16, 2025• 1 citation
Publisher

Abstract

In this paper, a series of electromagnetically-induced-transparent (EIT) spectra of different Rydberg states, controlled by microwaves, in rubidium (Rb) thermal vapor are presented. The novel evolution regularity for different Rydberg states can be found by experimentally detected transmitted EIT spectra, which can reveal the primary quantum number of different Rydberg states and how to influence microwave control spectroscopy evolution regularity, and which can pave the way in order to address the challenge of selecting Rydberg states for applications in Rydberg microwave field detection. This is helpful for the development of measuring standards of the microwave field in Rydberg states.

DOI
10.3390/photonics12070715

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In this paper, a series of electromagnetically-induced-transparent (EIT) spectra of different Rydberg states, controlled by microwaves, in rubidium (Rb) thermal vapor are presented. The novel evolution regularity for different Rydberg states can be found by experimentally detected transmitted EIT spectra, which can reveal the primary quantum number of different Rydberg states and how to influence microwave control spectroscopy evolution regularity, and which can pave the way in order to address the challenge of selecting Rydberg states for applications in Rydberg microwave field detection. This is helpful for the development of measuring standards of the microwave field in Rydberg states.
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.
Significant progress has been made in atom-based measurements of length, time, gravity and electromagnetic fields in recently years. Rydberg atom-based microwave electric field measurement, using electromagnetically induced transparency (EIT) in room temperature alkali-metal vapors, has been extensively investigated and aroused the broad interest. This approach may establish a new standard for the measurements of microwave (MW) and radio frequency (RF) electric fields.In this review, we describe the work on a new method of measuring electric fields based on quantum interference by using either cesium or rubidium atoms contained in a dielectric vapor cell. Rydberg atoms with principal quantum number n >>1 have large direct current (DC) polarizabilities and microwave transition dipole moments, thereby making them extremely sensitive to external electric fields. Using the Rydberg three-level EIT to detect the level splitting and shift that is induced by the external field, we can realize a rapid and robust self-calibration method of measuring the electric field in a frequency range from 0.01 GHz to 1000 GHz. For the MW electric field (frequency range > 1 GHz), the MW field causes the Rydberg states to split, known as an Autler-Townes splitting (A-T) effect when the applied microwave can resonate with adjacent Rydberg states. The MW coupled A-T splitting is proportional to the applied electric field strength, from which the field strength is measured. Using the EIT window, a high sensitivity of 3 μV·cm-1·Hz-1/2 and small electric field of 1 μV/cm are expected to be achieved with a modest setup, and the limitations of the sensitivity are also addressed in the review. For the RF field at frequency mj EIT lines, and avoided crossings formed with the fine-structure levels of equal mj and different J's, which is used to calibrate and measure the RF field amplitude. On the other hand, the dependence of the EIT-line strength on the RF field polarization provides a fast and robust polarization measurement of RF fields based on matching experimental data with a theoretical simulation. The measurements of minimum strengths and sensitivity of RF fields based on Rydberg atoms are one order magnitude below the values obtained by traditional antenna methods. The atom-based field measurement paves the way for determining fields through calibration-free, invariable atomic properties and miniaturization. We also propose its various potential applications in the future.
Introduction: Quantum light–matter interaction provides an excellent application of Rydberg levels. Rydberg states are special in the sense that they have a long lifetime and large dipole moments. The large number of these levels and the spacing among them enable the detection of the incoming signals in the broad region of the electromagnetic spectrum, encompassing microwave (MW), terahertz (THz) and radio frequency (RF) ranges. Electromagnetically Induced Absorption (EIA) and Transparency (EIT) can be achieved at these levels. MW and THz signals can quantum-mechanically split the relevant spectral lines in which the splitting is proportional to the strength of an incoming em field.
The spectral characteristics of the resonance effect of the electromagnetic-induced transparency (EIT) of rubidium atomic vapors induced by intense radiation with a wavelength in the region from 479 to 486 nm in the presence of microwave radiation at a frequency of 1 to 300 GHz, which splits the energy of transition of the atom from the resonant 5 P 3/2 states into the Rydberg nD 5/2 state, are determined. The magnitude of the splitting of the EIT peak is proportional to the electric field intensity of the microwave radiation. Simple approximation expressions are obtained for the numerical calculation of the transition amplitude between Rydberg nD 5/2 and ( n + 1) P 3/2 states with large principal quantum numbers n . A setup has been developed for measuring the electric field intensity of microwave radiation based on measuring the frequency of splitting of the resonance of an electron microscope in the absorption spectrum of probe radiation.