We present a combined experimental and Floquet-theoretical study of avoided crossings in the AC Stark-shifted electromagnetically induced transparency (EIT) spectra of Rydberg atoms. Observed avoided-crossing structures cannot be fully explained by conventional AC Stark maps alone, which provide the energy shifts but do not reveal the underlying state composition and coupling pathways. Using the Shirley method, we analyze the Floquet eigenstates to establish a direct connection between the measured spectra and the underlying dressed-state dynamics. By tracking the evolution of state mixing, bare-state composition, and dominant higher-order Floquet coupling pathways, we reveal the physical mechanisms responsible for the formation of avoided crossings across different principal quantum numbers and RF frequencies. Our results demonstrate that Floquet-eigenstate analysis provides a powerful framework for interpreting complex AC Stark-shifted Rydberg-EIT spectra and the underlying higher-order Floquet coupling interactions.
We present a combined experimental and Floquet-theoretical study of avoided crossings in the AC Stark-shifted electromagnetically induced transparency (EIT) spectra of Rydberg atoms. Observed avoided-crossing structures cannot be fully explained by conventional AC Stark maps alone, which provide the energy shifts but do not reveal the underlying state composition and coupling pathways. Using the Shirley method, we analyze the Floquet eigenstates to establish a direct connection between the measured spectra and the underlying dressed-state dynamics. By tracking the evolution of state mixing, bare-state composition, and dominant higher-order Floquet coupling pathways, we reveal the physical mechanisms responsible for the formation of avoided crossings across different principal quantum numbers and RF frequencies. Our results demonstrate that Floquet-eigenstate analysis provides a powerful framework for interpreting complex AC Stark-shifted Rydberg-EIT spectra and the underlying higher-order Floquet coupling interactions.
The large electric dipole moment of the Rydberg atom allows for strong coupling with weak electric fields, and is widely used in electric field measurements because of its reproducibility, precision and stability. The combination of Rydberg atoms and electromagnetically induced transparency (EIT) technology has been used for detecting and characterizing radio-frequency (RF) electric fields. In this work, by selecting probe light (852 nm), dressed light (1470 nm), and coupled light (780 nm), the Rydberg state (49P3/2) of Cs atom is prepared by using a three-photon excitation scheme through using all-infrared light excitation of Rydberg atoms. We experimentally observe the EIT spectra of the Rydberg states decorated by radio-frequency electric fields, which optically detects Rydberg atoms. The effect of the amplitude and frequency of the RF electric field on the spectrum is explored in light of changes in the EIT spectrum. The results show that in the region of weak electric field, only the ac Stark energy shift and spectral broadening occur. As the electric field is further enhanced, the sideband phenomenon occurs in both the primary peak and secondary peak of the EIT. In the region of strong field, the Rydberg energy level produces a series of Floquet states with higher-order terms, as well as state shifting and mixing, resulting in asymmetry in the spectra of the EIT sideband peaks. The effect of frequency on the shielding effect of the Cs vapor cell is further discussed based on the shift of the main peak of the EIT. The demodulation of the electric field in a range of 50 Hz–1 kHz with a fidelity of 95% is achieved by modulating the low-frequency electric field to the RF electric field. The results can provide valuable references for spectral detection and traceable measurements of low-frequency electric fields.
Rydberg atoms are highly excited atoms with large principal quantum number n, big sizes (~n2) and long lifetimes (~n3). Rydberg atoms are very sensitive to an external field due to the large polarizabilities of Rydberg atoms (~n7). Electromagnetically induced transparency (EIT) of Rydberg atom provides an ideal method to detect Rydberg atoms without destroying atoms, and can be used to measure the external direct current and radio frequency (RF) field. In this paper, we study the EIT effect of a cesium ladder-type three-level atom involving Rydberg state exposed to a weak RF field. The ground state (6S1/2), the excited state (6P3/2) and Rydberg state (48D5/2) constitute the Rydberg three-level system, in which the probe laser couples 6S1/2(F=4)6P3/2(F'=5) transition, whereas the coupling laser scans across the 6P3/248D5/2 Rydberg transition. The coupling laser (510 nm laser, propagating in the z-axis direction and linear polarization in the y-axis direction) and the probe laser (852 nm laser, linear polarization in the y-axis direction) counter-propagate through a 50-mm-long cesium vapor cell at room temperature, yielding Rydberg EIT spectra. Rydberg EIT signal is detected as a function of the detuning of the coupling laser. When a weak RF (80 MHz) electric field polarized in the x-axis direction is applied to a pair of electrode plates located on both sides of the cesium cell, the EIT spectrum of Rydberg 48D5/2 shows the Stark splitting and the even order harmonic sidebands. The experimental results are analyzed by using the Floquet theory. The simulation results accord well with the experimentally measured results. Furthermore, we also investigate the influence of the self-ionization effect of Rydberg atom on the Stark spectrum by changing the RF frequency. We put forward a proposal to avoid the effect of ionization by placing electrode plates in the cesium cell. In the weak RF-field domain, mj=5/2 Stark line crosses mj=1/2, 3/2 sidebands, these cross points provide an antenna-free method of accurately calibrating the RF electric field based on Rydberg atoms.
A Rydberg atom is a special type of atom characterized by a high principal quantum number. Electric field sensors based on Rydberg atoms have received widespread attention due to their high polarizability. However, there is currently little research on the use of Rydberg atoms for direct current (DC) or low-frequency electric fields, mainly due to the shielding effect of atomic vapor cells in low-frequency electric fields, which makes accurate measurement of the electric fields extremely challenging. In this paper, we construct a Rydberg ladder configuration by using probe laser at 852 nm and coupling laser at 510 nm in a room-temperature cesium vapor cell with integrated electrode plates, thereby enabling the realizing of a Floquet-EIT (electromagnetically induced transparency) spectrum dressed by a radio frequency (RF) field in the presence of a DC electric field. We further study the influence of DC electric field on spectral characteristic. Experimentally, it is observed that when only the RF electric field is applied, the EIT spectrum displays solely even-order sidebands. Furthermore, when both the RF field and the DC electric field are simultaneously present, the first-order sideband signal of the Floquet-EIT is observed. As the intensity of the DC electric field increases, the amplitude of the first-order sideband gradually increases. However, increasing the DC electric field to a sufficient magnitude induces sideband interference, which leads the sideband amplitudes to decrease. Furthermore, increasing the RF frequency can alleviate the interference effects induced by the DC electric field on the first-order sideband. Finally, comparing the relative standard deviation of the sideband amplitudes of the Floquet-EIT spectra with the frequency shifts of the DC-Stark spectra under weak DC electric fields, we find that the measurement accuracy of the former is significantly superior to that of the latter. This work makes use of a Cs atomic vapor cell with an integrated electrode to avoid shielding effects. By observing Floquet-EIT spectra, the response of the spectra to DC electric fields is investigated. This experiment provides novel insights into the quantum sensing measurements of DC and low-frequency electric fields.
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 initially discuss the theory of three-level systems using the dressed state formalism. One of the dressed states, containing a ground state and a Rydberg state, does not couple with the probe laser; thus, the medium becomes transparent to the latter. This phenomenon is known as electro- magnetically induced transparency (EIT) and this dressed state is known as a Rydberg dark state. We show that EIT can be used to extract the reduced dipole matrix element for transitions to a Rydberg state. However, a prob- lem with three-level Rydberg EIT in a vapour cell is the occurrence of space charges caused by photoelectric ionisation of Rb metal deposited inside the cell. To avoid this problem, we consider adding a third laser resonant with a fourth level. This is to avoid using the laser whose wavelength is less than the threshold wavelength. In cold atoms, the effect of the third laser is to split the usual EIT resonance into a doublet. In thermal atoms, we observe narrow features due to electromagnetically induced absorption and electro- magnetically induced transparency in the Doppler-free configuration. Next we consider the action of a far off-resonance radio frequency (rf) field in the three-level system. We demonstrate the formation of rf-dressed EIT reso- nances in a thermal Rb vapour and show that such states exhibit enhanced sensitivity to dc electric fields compared to their bare counterparts. Fitting the corresponding EIT profile enables precise measurements of the dc field in- dependent of laser frequency fluctuations. We further investigate the theory of rf-dressed Rydberg EIT using the Floquet approach in order to understand the formation of the sideband structure of the Rydberg state. We find that if the time scale of the rf interaction is much shorter than that of the system evolution and decoherence, the sideband structure is well resolved. We also show that the intermediate state exhibits a sideband structure, induced by the Rydberg state, when the Rabi frequency of coupling laser is larger than twice the modulation frequency. Finally we consider resonant microwave cou- pling between the Rydberg states which leads to an Autler-Townes splitting of the EIT resonance in cold atoms. This splitting can be employed to vary the group index by ±10^5 allowing independent control of the absorptive and dispersive properties of the medium, i.e., one can switch the transparency of the medium or control the group velocity of a pulse propagation by tuning on and off the microwave field.
We design phase-sensitive Rydberg-atom interferometry by implementing Floquet electromagnetically induced transparency (FEIT). The FEIT mixes the sidebands of a Rydberg state induced by a megahertz radio frequency (rf) field and recombines them into FEIT bands. The FEIT bands act as screens to present the interference between paths with different phases, which are transitions between the sidebands and excited states. This interferometry can measure the phase of a megahertz rf field without a local rf reference field. A phase reference is supplied to the atoms via a periodic electrical signal in the FEIT. We demonstrate that the megahertz rf phase can be resolved over the full $2\ensuremath{\pi}$ range with a theoretical accuracy of ${10}^{\ensuremath{-}4}$ rad. Moreover, the rf amplitude can also be resolved with higher accuracy than with the traditional EIT-based scheme.