Abstract A ready-to-use numerical model has been developed for the atomic ladder (cascade) systems which are widely exploited in Rydberg Radio Frequency (RF) sensors. The model has been explicitly designed for user convenience and to be extensible to arbitrary N-level non-thermal systems. The versatility and adaptability of the model is validated up to 4-level atomic systems by direct comparison with experimental results from the prior art. The numerical model provides a good approximation to the experimental results and provides experimentalists with a convenient ready-to-use model to optimise the operation of an N-level Rydberg RF sensor. Current sensors exploit the 4-level atomic systems based on alkali metal atoms which require visible frequency lasers and these can be expensive and also suffer from high attenuation within optical fiber. The ability to quickly and simply explore more complex N-level systems offers the potential to use cheaper and lower-loss near-infrared lasers.
Abstract A ready-to-use numerical model has been developed for the atomic ladder (cascade) systems which are widely exploited in Rydberg Radio Frequency (RF) sensors. The model has been explicitly designed for user convenience and to be extensible to arbitrary N-level non-thermal systems. The versatility and adaptability of the model is validated up to 4-level atomic systems by direct comparison with experimental results from the prior art. The numerical model provides a good approximation to the experimental results and provides experimentalists with a convenient ready-to-use model to optimise the operation of an N-level Rydberg RF sensor. Current sensors exploit the 4-level atomic systems based on alkali metal atoms which require visible frequency lasers and these can be expensive and also suffer from high attenuation within optical fiber. The ability to quickly and simply explore more complex N-level systems offers the potential to use cheaper and lower-loss near-infrared lasers.
In this work, theoretical and experimental works on Rydberg-atom based radio-frequency (RF) sensors are presented. The results were obtained in close collaboration with the Quantum Valley Ideas Lab, whose goal is the miniaturization and prototyping of these sensors. The Rydberg-atom based RF sensors utilize lasers to coherently excite an atomic vapor in a vapor cell at room temperature to a highly excited Rydberg state, which is extremely sensitive to external environmental influences. In this work, Rydberg-atom based RF sensing is described as coherent multi-photon interference in the atom-light coupled system by introducing atom-light coherences. The presence of the RF wave influences the absorption of a probe laser propagating through the atomic medium. The atomic response of the Rydberg-atoms can be engineered by changing the atom-light coherences through laser power and frequency. Analytic expressions for the atomic response to the incident RF wave are derived in the weak probe limit and provide a deeper understanding of the underlying coherent multi-photon interference processes, which help to further tailor the Rydberg-atom for the purpose of the application. Good agreement with full numerical simulations of the Lindblad-master equation is found. An analysis of the various Doppler limits strongly motivates an excitation scheme where the effective wave vector mismatch on the Rydberg transition vanishes, as a promising candidate to achieve narrower spectral linewidths and, consequently, a higher sensitivity. The level structure of cesium presents a unique three-photon excitation scheme where residual Doppler shifts become comparable to the spectral linewidth of the coupling lasers. The experimental realization of this excitation scheme is demonstrated. A spectral linewidth of the Rydberg transition of 190 kHz is achieved. The measurements present the world record sensitivity, 45 nV/cm/Hz^1/2, for all-optical RF sensing with room temperature operation. These results make the three-photon excitation scheme a prime candidate for the next generation of Rydberg-atom based RF sensor prototypes. Finally, all-optical phase-sensitive RF detection is theoretically investigated in a closed-loop excitation scheme. An analytic expression is derived that intuitively describes the atomic response. Furthermore, it provides insights into the probe intensity dynamics that occur when the system is operated under finite detuning. These oscillatory dynamics allow for the extraction of the in- (I) and out- (Q) of-phase response to the RF wave, thereby enabling the simultaneous detection of the RF E-field amplitude and phase. A blueprint for the experimental realization is presented, and angle-of-arrival tolerances for the RF wave are estimated. A quadrature amplitude modulation (QAM) sequence was modelled and the simultaneous extraction of the phase and amplitude of the RF wave of interest was successfully demonstrated.
Quantum Rydberg atom-based radio frequency (RF) sensors exploit the exceptional sensitivity of highly excited atomic states to detect electromagnetic fields with very high precision, offering potential advances in telecommunications, radar and microwave radiometer systems, GNSS-Reflectometers, and electromagnetic compatibility testing. This study presents a detailed MATLAB simulation analysis of radio-frequency sensors modeled as a five-level rubidium-87 (Rb-87) system under the influence of RF and optical fields. The simulation leverages the Lindblad master equation to capture the coherent evolution, the spontaneous emission, the collisional dephasing, and the field-induced ionization. For an external RF electric field of E0 = 100 mV/m, a frequency sweep from 10MHz to 10GHz reveals the impact of noise: an ideal case just limited by quantum noise yields a sensitivity of 0.01 µV/m/ v Hz and a SNR of 177dB, while for E0 = 10 mV/m and a realistic noise (-130 dBm/Hz) the sensitivity worsens to 72 - 633 µV/m/ v Hz and a SNR of 72 dB. The study investigates the effects of RF field amplitude, atom density, and environmental parameters such as residual magnetic field and ambient temperature, in the sensitivity and bandwidth of these promising receivers, offering a framework to optimize Rydberg-based sensing technologies for Earth Observation, Communication and Navigation systems.
We present a theoretical and experimental investigation of the improvement and determination of the sensitivity of Rydberg atom-based microwave RF sensor. An optical Bloch equation has been set up based on the configuration that two-color cascading lasers exciting atom to highly Rydberg state and a microwave RF coupling this Rydberg state to its adjacent neighbor. The numerical simulation shows that the sensitivity of the atomic RF sensor is correlated with the amplitude strengths of the applied two lasers and the RF itself. It also depends on the frequency detuning of the coupling laser, which induces an asymmetrically optical splitting. The coupling laser frequency fixing at the shoulder of the stronger one is more favorable for a higher sensitivity. Accordingly, we perform an experimental demonstration for the optimization of all these parameters and the sensitivity is improved to 12.50(04) nVcm−1·Hz−1/2.
Rydberg-atom-based electrometry provides a quantum, SI-traceable approach to radio-frequency (RF) and microwave electric-field sensing by linking optical spectra to absolute field strength through electromagnetically induced trans parency. Over the past decade, rapid advances in excitation schemes, field-tuning methods, interferometric readout, and cavity-assisted coupling have significantly improved sensitivity, bandwidth, and tunability of Rydberg-based sensors. In parallel, progress in fiber-coupled modules, microfabricated vapor cells, and photonic integration is enabling compact and deployable receiver architectures. This review presents a comprehensive and metrology-oriented synthesis of the physical principles, system architectures, standardized performance metrics, and uncertainty considerations relevant to Rydberg-atom RF sensing. By con solidating diverse developments into a unified performance and evaluation framework, this work provides a critical reference for the design, comparison, and advancement of next-generation quantum RF sensors and standards.
Rydberg atom-based radio frequency electromagnetic field sensors are drawing wide-spread interest because of their unique properties, such as small size, dielectric construction, and self-calibration. These photonic sensors use lasers to prepare atoms and read out the atomic response to a radio frequency electromagnetic field based on electromagnetically induced transparency, or related phenomena. Much of the theoretical work has focused on the Autler-Townes splitting induced by the radio frequency wave. The amplitude regime, where the change in transmission observed on resonance is measured to determine electric field strength, has received less attention. In this paper, we deliver analytic expressions that are useful for calculating the absorption coefficient in the amplitude regime. Our main goal is to describe the analytic expressions for the absorption coefficient and demonstrate their validity over a large range of the interesting parameter space. The effect of the thermal motion of the atoms is explicitly addressed. The analytic formulas for the absorption coefficient for different types of Doppler broadening are compared to estimate the sensitivity under conditions where it is limited by the laser shot noise. Residual Doppler shifts are shown to limit sensitivity. The expressions, approximations and descriptions presented in the paper are important for understanding the absorption of Rydberg atom-based sensors in the amplitude regime. This provides insight into the physics of multi-level interference phenomena.
Multi-photon dressing and interference in atomic systems is a key to several cutting edge technologies like Rydberg atom radio frequency sensors, clocks and magnetometers because it enables the engineering of atomic properties. Rydberg atom sensors are attracting significant interest because they can be used for applications where it is difficult or impossible to use conventional antennas, opening a number of new opportunities in fields like communications, test and measurement and radar. To date, radio frequency field amplitude detection is well-established in Rydberg electrometry. Phase detection, which is crucial for encoding radio frequency signals, typically requires an external heterodyning field or an atomic closed-loop interferometer. The heterodyne method compromises the intrinsic transparency of the sensor to the radio frequency wave and its inherently broad carrier bandwidth, in addition to increasing its complexity by introducing a local oscillator. In prior theoretical work, aimed at overcoming the disadvantages of the heterodyne method, we theoretically investigated the possibility of using the oscillatory dynamics of an all-optical five-level closed loop to sense the phase and amplitude of the target radio frequency fields. In this work, we experimentally demonstrate the scheme. We determine the coherence time of the loop to be on the order of ms and show that in-phase and quadrature signals can be extracted from a radio frequency signal.