Energy levels of Rydberg Rubidium atoms in an external electric field are calculated by Hamiltonian-diagonalization and Coulomb approximation. The results are in agreement with previous studies and with the expected scaling laws. Comparing to electromagnetically induced transparency(EIT) experiments of Rubidium vapour in 90 MHz rf electric field and room temperature of Durham University, we can observe the effect of the presence of ions and oscillating electric field. The BIT experimental results also show larger effective field than theoretical results by a factor of 1.35.
Energy levels of Rydberg Rubidium atoms in an external electric field are calculated by Hamiltonian-diagonalization and Coulomb approximation. The results are in agreement with previous studies and with the expected scaling laws. Comparing to electromagnetically induced transparency(EIT) experiments of Rubidium vapour in 90 MHz rf electric field and room temperature of Durham University, we can observe the effect of the presence of ions and oscillating electric field. The BIT experimental results also show larger effective field than theoretical results by a factor of 1.35.
We report on the measurement of Stark shifted energy levels of 87 Rb Rydberg atoms in static electric fields by means of electromagnetically induced transparency (EIT). Electric field strengths of up to 500 V cm −1 , ranging beyond the classical ionization threshold, were applied using electrodes inside a glass cell with rubidium vapour. Stark maps for principal quantum numbers n = 35 and n = 70 have been obtained with high signal-to-noise ratio for comparison with results from ab initio calculations following the method described in (Zimmerman et al 1979 Phys. Rev. A 20 2251 ), which was originally only verified for states around n = 15. We also calculate the dipole matrix elements between low-lying states and Stark shifted Rydberg states to give a theoretical estimate of the relative strength of the EIT signal. The present work significantly extends the experimental verification of this numerical method in the range of both high principal quantum numbers and high electric fields with an accuracy of up to 2 MHz.
We present experimental results on the influence of magnetic fields and laser polarization on electromagnetically induced transparency (EIT) using Rydberg levels of ^{87} 87 Rb atoms. The measurements are performed in a room temperature vapor cell with two counter-propagating laser beams at 480 m and 780 m in a ladder-type energy level scheme. We measure the EIT spectrum of a range of ns_{1/2} n s 1 / 2 Rydberg states for n=19-27 n = 19 − 27 , where the hyperfine structure can still be resolved. Our measurements span the range of magnetic fields from the low field linear Zeeman regime to the high field Paschen-Back regimes. The observed spectra are very sensitive to small changes in magnetic fields and the polarization of the laser beams. We model our observations using optical Bloch equations that take into account the full multi-level structure of the atomic states involved and the decoupling of the electronic J J and nuclear I I angular momenta in the Breit-Rabi regime. The numerical model yields excellent agreement with the observations. In addition to EIT related experiments, our results are relevant for experiments involving coherent excitation to Rydberg levels in the presence of magnetic fields.
We study Rydberg atoms modulated by strong radio-frequency (rf) fields with a frequency of 70 MHz. The Rydberg atoms are prepared in a room-temperature cesium cell, and their level structure is probed using electromagnetically induced transparency (EIT). As the rf field increases from the weak- into the strong-field regime, the range of observed rf-induced phenomena progresses from ac level shifts through increasingly pronounced and numerous rf modulation sidebands to complex state mixing and level crossings with $\mathrm{high}\ensuremath{-}l$ hydrogenlike states. Weak anharmonic admixtures in the rf field generate clearly visible modifications in the Rydberg EIT spectra. A Floquet analysis is employed to model the Rydberg spectra, and good agreement with the experimental observations is found. Our results show that all-optical spectroscopy of Rydberg atoms in vapor cells can serve as an antenna-free, atom-based, and calibration-free technique to measure rf electric fields and to analyze their higher-harmonic contents.
Abstract Atom-based electromagnetic field sensing is a highly precise and sensitive technique for measuring and detecting electromagnetic fields, based on the principles of the Rydberg electromagnetically induced transparency (EIT). In this study, we simulate an atom-based electric field measurement system using a four-level system of rubidium atoms. We solve the steady-state solution of the Lindblad master equation using a Hamiltonian that contains information about rubidium properties and the external electric field. We observe that the splitting of the EIT signal is directly proportional to the intensity of the applied electric field, making it a highly sensitive method for electromagnetic field sensing. In addition, we investigate the effect of laser detuning and Rabi frequency on the linewidth and signal strength of the EIT signal in order to obtain optimal parameters for future experiments. This study provides insights into optimizing the EIT signal for electromagnetic fields detection, with potential benefits for future developments in this field.
In this work, numerical calculations were implemented based on the diagonalisation of a matrix representation of the Stark Hamiltonian on a subset of the basis given by the zero-field Hamiltonian. Dipole matrix elements between the involved states were calculated, which allow for the prediction of transition strengths to Stark shifted Rydberg states. The applicability of the numerical methods were confirmed experimentally by precision spectroscopy in a rubidium vapour cell with electrodes using electromagnetically induced transparency (EIT). The numerical methods were then extended to predict ionisation rates of Rydberg states in the highly Stark shifted regime beyond the classical ionisation threshold. For this purpose, a complex absorbing potential (CAP) was specifically adjusted to the Stark Hamiltonian. An experiment was conducted, in which cold atoms from a magneto-optical trap (MOT) were excited to Stark shifted Rydberg states and the arising ions were detected. The obtained ionisation spectra agree well with the results from the numerical calculations. Another extension of the numerical methods was implemented for crossed electric and magnetic fields. This was used for approximate calculations of the motional Stark effect (MSE), which acts on atoms moving through static magnetic fields and thereby experiencing a Lorentz electric field. In a precision spectroscopy, once more using EIT in a vapour cell, the MSE was observed in low magnetic fields for the first time in rubidium. The spectral shift, which is caused by the MSE, matches the prediction from the numerical calculations. In a final experiment, the practical use of the knowledge of several properties of Stark shifted Rydberg states was illustrated. The numerical methods including the CAP were used to specifically select states for their optical accessibility, permanent electric dipole moments and ionisation rates. In the experiment, atoms from a MOT were excited to these states to observe different characteristics of the dipole blockade effect. The detection scheme for this experiment was realised by controlled ionisation using only small changes in the external electric field.
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.