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Journal of the Optical Society of America B

Transitions between triplet Rydberg states of the alkaline-earth-metal atoms for precision measurements of microwave fields

Igor L. Glukhov, Aleksandr A. Kamenski, A. S. Kornev, Nikolai L. Manakov, Vitaly D. Ovsiannikov, Vitaly G. Palchikov

Published Jul 23, 2024• 0 citations
Publisher

Abstract

We calculated the frequencies and amplitudes of the microwave (µw) dipole transitions between triplet Rydberg states of n 3 S 1 , n 3 P 1 , n 3 D 2 , and n 3 F 3 series in the alkaline-earth atoms. Numerical values of the amplitudes determine the µw electric-field-dependent Rabi frequency of the Rydberg level shift in the field of a resonance radiation. This shift, observed as splitting of resonance in electromagnetically induced transparency for intensely absorbed probe radiation, enables measuring the µw electric field strength. For numerical calculations, we used single-electron methods and the most reliable data on quantum defect values from the literature. We derived the asymptotic approximation formulas of the µw frequencies and amplitudes.

DOI
10.1364/josab.527704

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We calculated the frequencies and amplitudes of the microwave (µw) dipole transitions between triplet Rydberg states of n 3 S 1 , n 3 P 1 , n 3 D 2 , and n 3 F 3 series in the alkaline-earth atoms. Numerical values of the amplitudes determine the µw electric-field-dependent Rabi frequency of the Rydberg level shift in the field of a resonance radiation. This shift, observed as splitting of resonance in electromagnetically induced transparency for intensely absorbed probe radiation, enables measuring the µw electric field strength. For numerical calculations, we used single-electron methods and the most reliable data on quantum defect values from the literature. We derived the asymptotic approximation formulas of the µw frequencies and amplitudes.
Abstract Background of the electromagnetically induced transparency (EIT) resonance splitting by millimeter-wave radiation was investigated and so were calculated frequencies and amplitudes of radiation transitions between Rydberg states in alkaline earth atoms of IIA group elements, which are necessary for precise measurements of electric field magnitude at millimeter-wave (mmw) frequencies. Numerical values of the frequencies and matrix elements are approximated by asymptotic polynomials and tabulated for dipole transitions between singlet nS, nP, nD, and nF states with large values of principal quantum number n.
The high-precision determination of microwave radiation parameters may be based on measurements of the spectral characteristics of radiation transitions between the Rydberg states of atoms. Frequencies and matrix elements are calculated for dipole transitions from even-parity nS1/2 and nD5/2 to odd-parity n′P3/2 and n′F7/2 (where n′ = n, n ± 1, n ± 2) for the Rydberg states of alkali-metal atoms. The matrix elements determine the splitting of Rydberg-state energy levels in the field of a resonance microwave (μw) radiation, which results in the splitting of the resonance in electromagnetic induced transparency (EIT). Numerical computations based on the single-electron quantum defect method (QDM) and the Fues’ model potential (FMP) approach with the use of the most reliable data of the current literature on quantum defect values were performed for the 2S, 2P, 2D and 2F series of the Rydberg states of Li, Na, K, Rb and Cs atoms. The calculated data were approximated by quadratic polynomials of the principal quantum number. The polynomial coefficients were determined with the use of a standard curve-fitting interpolation polynomial procedure for numerically presented functions. The approximation equations may be used for the accurate evaluation of the frequencies and matrix elements of μw transitions in wide ranges of the Rydberg-state quantum numbers n >> 1.
Background of the electromagnetically induced transparency (EIT) resonance splitting by millimeter-wave radiation was investigated and so were calculated frequencies and amplitudes of radiation transitions between Rydberg states in alkaline earth atoms of IIA group elements, which are necessary for precise measurements of electric field magnitude at millimeter-wave (mmw) frequencies. Numerical values of the frequencies and matrix elements are approximated by asymptotic polynomials and tabulated for dipole transitions between singletnS,nP,nD, andnF states with large values of principal quantum numbern.
The measurements of microwave (μw) and radio-frequency (RF) radiation quantitative parameters may be based on the quantum–optical approach to determine the spectral characteristics of radiation transitions between the Rydberg states of atoms. Frequencies and matrix elements are calculated for dipole transitions between opposite-parity Rydberg states nL 1L and n′L±1 1L±1 (where n′= n,n±1,n±2) of the singlet series in the alkaline–earth–metal-like atoms of group IIb (Zn, Cd, Hg) and Yb. The matrix elements determine the shifts of Rydberg-state energy levels in the field of resonance μw or RF radiation, splitting the resonance of electromagnetically induced transparency (EIT) for intensely absorbed probe radiation. Numerical computations based on the single-electron quantum defect method (QDM) and the Fues’ model potential (FMP) approach with the use of the most reliable data from the current literature on quantum defect values are performed for frequencies and matrix elements of transitions between singlet Rydberg states of 1S0-, 1P1-, 1D2-, and 1F3-series in Zn, Cd, Hg, and Yb atoms. The calculated data are approximated by polynomials in the powers of the principal quantum numbers. The polynomial coefficients are determined with the use of a standard curve-fitting interpolation polynomial procedure for numerically calculated functions. These approximation expressions provide new possibilities for accurately evaluating the frequencies and matrix elements of dipole transitions between Rydberg states over a wide range of quantum numbers n >> 1, accompanied by the emission and absorption of μw and RF photons.
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.
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.