We investigate the electromagnetically induced transparency (EIT) and Autler Townes (AT) splitting spectrum with a four-level Rydberg atom by pole analysis of the probe coherence. A pair of poles corresponding to the two peaks of the spectral splitting is observed. The spectral split or the pole positions are affected by the microwave intensity (MW) and the detuning between the probe and the coupling laser. In the absence of any detuning, the two poles coincide and separate again on the imaginary axis of the complex detuning plane at weak MW field. The two poles do not coincide when the probe (coupling) laser is detuned for scanning the coupling (probe) laser frequency. However, under finite detuning, the two poles approach the nearest distance in the absence of any splitting and are separated again in the direction parallel to the imaginary axis. The spectral analysis of the poles provides an alternate way to establish the relationship between the splitting and the intensity of MW, which may play a role in the application of atomic-based MW measurements.
We investigate the electromagnetically induced transparency (EIT) and Autler Townes (AT) splitting spectrum with a four-level Rydberg atom by pole analysis of the probe coherence. A pair of poles corresponding to the two peaks of the spectral splitting is observed. The spectral split or the pole positions are affected by the microwave intensity (MW) and the detuning between the probe and the coupling laser. In the absence of any detuning, the two poles coincide and separate again on the imaginary axis of the complex detuning plane at weak MW field. The two poles do not coincide when the probe (coupling) laser is detuned for scanning the coupling (probe) laser frequency. However, under finite detuning, the two poles approach the nearest distance in the absence of any splitting and are separated again in the direction parallel to the imaginary axis. The spectral analysis of the poles provides an alternate way to establish the relationship between the splitting and the intensity of MW, which may play a role in the application of atomic-based MW measurements.
To distinguish the contributions of electromagnetically induced transparency (EIT) and Autler-Townes splitting (ATS) in their applications in precision laser spectroscopy, we propose a real-imaginary spectrum decomposition method to investigate the transparency spectra in a four-level microwave (MW) dressed Rydberg system. We show that the opening transparency windows in the absorption spectra of probe field is a prominent character by EIT, EIT-ATS crossover, and ATS when the MW field is turned off and the intensity of the control field is adjusted. When the MW field is turned on and gradually increased, the EIT is destroyed and disappears. In addition, the most prominent characters that open a transparency window are the EIT-ATS crossover and the ATS. Then, if we further increase the intensity of the MW field, we find that the transparency windows open mainly due to the ATS. Compared to the previous considerations of this issue, which were limited to three-level systems, our four-level scheme reported here is useful for understanding the features of quantum interference in multilevel atomic systems, and has potential applications to study enhanced sensitivity, measurement spectroscopic, quantum processing, quantum communication, and transmission.
An analytical model of an electromagnetically induced transparency (EIT) and Autler–Townes (AT) splitting spectrum with a four-level Rydberg atom was presented, and equations were derived to explain the dependence of the transient absorption for a probe laser on light and microwave (MW) fields. The analytical solution of absorption for the probe laser Im [ χ ( t )] shows that it depends on the spontaneous decay rate from level |2〉 to level |1〉, Rabi frequencies of the control and MW fields. For 87 Rb atoms, a stronger control laser shortens the steady-state time window and a stronger MW field will lead to a higher oscillation frequency shown in analytical and numerical results. The time-dependent EIT-AT splitting spectrum is also investigated, and the stable splitting distance shows a linear dependence on the continuous MW E-field strength.
An electromagnetically induced transparency (EIT) of a cascade-three-level atom involving Rydberg level in a room-temperature cell, formed with a cesium 6S 1 / 2-6P 3 / 2-66 S 1 / 2 scheme, is employed to detect the Autler-Townes (AT) splitting resulted with a 15.21-GHz microwave field coupling the 66 S 1 / 2 → 65 P 1 / 2 transition. Microwave field induced AT splitting, f A T, is characterized by the distance of peak-to-peak of an EIT-AT spectrum. The f A T dependence on the microwave Rabi frequency, Ω M W , demonstrates two regions, the strong-coupling linear region, f A T ≈ Ω M W and the weak-coupling nonlinear region, f A T ≲ Ω M W. The f A T dependencies on the probe and coupling Rabi frequency are also investigated. Using small probe- and coupling-laser, the Rabi frequency is found to enlarge the linear regime and decrease the uncertainty of the microwave field measurements. The measurements agree with the calculations based on a four-level atomic model.
We present an electromagnetically induced transparency and Aulter-Townes (EIT-AT) spectrum of a Rydberg three-level atom that is dressed with a microwave field in a room-temperature cesium cell. The EIT is a quantum coherent effect produced by the interaction of atoms with electromagnetic waves, which leads to the decrease of the absorption for a weak resonant probe laser. AT splitting refers to the phenomenon, that the absorption line splits when an electromagnetic field that is in resonance or near resonance acts on the transition of atoms. Rydberg atoms are extremely sensitive to an external electric field due to their large polarizabilities and microwave transition dipole moments, which can be used to measure the external field. In this work, a Rydberg three-level EIT is used to detect Rydberg atom and AT splitting induced by the microwave field. Cesium levels 6S1/2, 6P3/2 and 50S1/2 constitute a Rydberg three-level system, in which a weak probe laser locking to the transition from 6S1/2 to 6P3/2 couples ground-state transition and the strong coupling laser resonates on the Rydberg transition from 6P2/3 to 50S1/2. The two Rydberg levels 50S1/2 and 50P1/2 are coupled with the microwave field at a frequency of 30.852 GHz, leading to the AT splitting of EIT line and forming an EIT-AT spectrum, which is used to measure the electric field amplitude of microwave. In order to further study the EIT-AT splitting characteristics of the Rydberg levels, we carry out a series of measurements by changing the microwave field. The experimental results show a broadened EIT-AT signal for the weak field range and the four-peak spectrum for the strong field, which is attributed to the inhomogeneity of the microwave field. The microwave in cesium cell, emitted by a function generator, shows inhomogeneous behavior such that the atoms interacting with the laser field experience the different fields, leading to the line broadened and multi-peak EIT-AT spectra. For the microwave transition of nS1/2-nP1/2 in this paper, a pair of EIT-AT lines should be obtained for an electric field value. The broadening of the EIT-AT spectrum and the multi-peak structure here are due to the inhomogeneity of the microwave field measurement. We propose a method to increase the spatial resolution by reducing the length of cesium cell. The result in this work provides a method of measuring the field amplitude and monitoring the distribution of microwave electric field, meanwhile the spatial resolution of the measurements can be improved by reducing the size of the cell.
Abstract We theoretically and experimentally studied quantum microwave electrometry in a cold atomic system using Rydberg electromagnetic induction transparency (EIT) and Autler–Townes splitting (EIT-AT splitting). In cold atoms, a spectral linewidth of ∼500 kHz for EIT was achieved owing to a significant reduction in residual Doppler width, i.e. by at least an order of magnitude, compared to that in vapor cells at room temperature. Therefore, the minimum microwave electric field intensity (E MW) that can be measured is 430 µV cm−1, which is one order higher sensitivity in the EIT-AT regime than that in vapor cells at room temperature. Unlike microwave electrometry in atomic vapor cells, EIT-AT splitting cannot be observed if E MW is so large that the EIT-AT splitting interval Δ f m exceeds the absorption peak width of the cold atom while scanning the frequency of the probe laser (ω p ). Moreover, EIT-AT splitting can be observed if Δ f m exceeds the natural linewidth Γ eg of the intermediate states while scanning the coupling laser (ω c ) and maintains a high spectral resolution with a high signal-to-noise ratio. While scanning ω c , the upper microwave electric field intensity is limited by the scanning range of our setup. Using our system, we measure the maximum field to be 21.6 mV cm−1, nearly three times higher than that of 6.8 mV cm−1 while scanning ω p . The results indicate that the linear range of E MW measured using EIT-AT splitting considerably improves in cold Rydberg atoms.
We theoretically and experimentally investigate the Rydberg electromagnetically induced transparency (EIT) and Autler-Townes (AT) splitting of 87 Rb vapor under the combined influence of a magnetic field and a microwave field. In the presence of static magnetic field, the effect of the microwave field leads to the dressing and splitting of each m F state, resulting in multiple spectral peaks in the EIT-AT spectrum. A simplified analytical formula was developed to explain the EIT-AT spectrum in a static magnetic field, and the theoretical calculations agree qualitatively with experimental results. The Rydberg atom microwave electric field sensor performance was enhanced by making use of the splitting interval between the two maximum absolute m F states separated by the static magnetic field, which was attributed to the stronger Clebsch-Gordon coefficients between the extreme m F states and the frequency detuning of the microwave electric field under the static magnetic field. The traceable measurement limit of weak electric field by EIT-AT splitting method was extended by an order of magnitude, which is promising for precise microwave electric field measurement.