We demonstrate the use of an auxiliary microwave field to extend the bandwidth sensitivity of Rydberg-atom-based microwave electrometry. Electromagnetically induced transparency (EIT) and Autler-Townes (AT) splitting in Rydberg atom microwave electrometry provide advantageous sensitivity for the resonant detection of microwave (MW) fields because the Stark shift of the target Rydberg state takes the linear form of AT splitting. However, the sensitivity is reduced by several orders of magnitude for detuned MW fields because the Stark shift of the target Rydberg state depends on a weak nonlinear effect. We show that the auxiliary microwave field with appropriate Rabi frequency or detuning could shift the atomic energy levels to bring a particular Rydberg-Rydberg transition of interest for microwave sensing into resonance with the target microwave field. Using the atomic superheterodyne method, we verified the general method that regulates Rydberg energy levels using an auxiliary microwave field. The experimental results of this study confirm that this technique works efficiently for detecting microwave fields detuned by up to 100 MHz from resonance with the field-free Rydberg-Rydberg transition used for sensing. The measurement sensitivity of the detuned target field is increased by a factor of 10 compared with that achieved without the application of the auxiliary dressing field.
The atom-based traceable standard for microwave electrometry shows promising advantages by enabling stable and uniform measurement. Here we theoretically propose and then experimentally realize an alternative direct International System of Units (SI)--traceable and self-calibrated method for measuring a microwave-electric-field strength based on electromagnetically induced absorption (EIA) in cold Rydberg atoms. Comparing with the method of electromagnetically induced transparency, we show that the equivalence relation between the microwave Rabi frequency and Autler-Townes splitting is more valid and is even more robust against the experimental parameters in the EIA's linear region. Furthermore, a narrower linewidth of cold Rydberg EIA enables us to realize a direct SI-traceable microwave-electric-field measurement as small as $\ensuremath{\sim}100\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{V}\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$.
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 have theoretically and experimentally studied the dispersive signal of the Rydberg atomic electromagnetically-induced transparency (EIT) Autler–Townes (AT) splitting spectra obtained using amplitude modulation of the microwave (MW) electric field. In addition to the two zero-crossing points interval Δf zeros, the dispersion signal has two positive maxima with an interval defined as the shoulder interval Δf sho, which is theoretically expected to be used to measure a much weaker MW electric field. The relationship of the MW field strength E MW and Δf sho is experimentally studied at the MW frequencies of 31.6 GHz and 9.2 GHz respectively. The results show that Δf sho can be used to characterize the much weaker E MW than that of Δf zeros and the traditional EIT–AT splitting interval Δf m; the minimum E MW measured by Δf sho is about 30 times smaller than that by Δf m. As an example, the minimum E MW at 9.2 GHz that can be characterized by Δf sho is 0.056 mV/cm, which is the minimum value characterized by the frequency interval using a vapor cell without adding any auxiliary fields. The proposed method can improve the weak limit and sensitivity of E MW measured by the spectral frequency interval, which is important in the direct measurement of weak E MW.
We have theoretically and experimentally studied the dispersive signal of the Rydberg atomic electromagnetically induced transparency (EIT) - Autler-Townes (AT) splitting spectra obtained using amplitude modulation of the microwave (MW) field. In addition to the two zero-crossing points, the dispersion signal has two positive maxima with an interval defined as the shoulder interval of the dispersion signal
Δfsho. The relationship of MW field strength
EMW and
Δfsho are studied at the MW frequencies of 31.6 GHz, 22.1 GHz, and 9.2 GHz respectively. The results show that
Δfsho can be used to character the much weaker
EMW than the interval of two zero-crossing points
Δfzeros and the traditional EIT-AT splitting interval
Δfm, the minimum
EMW measured by
Δfsho is about 30 times smaller than that by
Δfm. As an example, the minimum
EMW at 9.2 GHz that can be characterized by
Δfsho is 0.056 mV/cm, which is the minimum value characterized by frequency interval using vapour cell without adding any auxiliary fields. The proposed method can improve the weak limit and sensitivity of
EMW measured by spectral frequency interval, which is important in the direct measurement of weak
EMW.
We provide the simultaneous traceable measurements of microwave electric fields at two different frequencies by the electromagnetically induced transparency (EIT) and Autler–Townes (AT) splitting. A static magnetic field working together with a linearly polarized probe and coupling light prepares Rydberg atoms in Zeeman sublevels with maximal |mJ| in an atomic vapor cell. Using the EIT-AT splitting of these two maximal |mJ| states, the microwave electric fields at two different frequencies are simultaneously measured, in which their frequency difference can be adjustable within the linear range of magnetic field-induced level shifts. The proposed method provides a promising prospect for calibrating multiple microwave frequencies simultaneously in the future.