In recent years, quantum electric field sensing technology based on Rydberg atoms has developed rapidly. Although some studies have begun to focus on the time evolution of two-photon-atom interactions and have conducted preliminary discussions on the transient behavior of EIT systems, most of the work still solves the EIT driving equation under the steady-state assumption and pays insufficient attention to the complete response process of atoms to the external electric field. In order to further fill this research gap, we formulate a density-matrix model for a ladder-type three-level Rydberg system and solve the EIT-driven equations under non-steady-state conditions. Numerical simulations reveal the real-time evolution of the atomic response during two-photon excitation and elucidate how various system parameters shape this response. On this basis, we identify optimal parameter settings that enhance the real-time performance of Rydberg-atom quantum measurements and provide theoretical guidance for future sensor design.
In recent years, quantum electric field sensing technology based on Rydberg atoms has developed rapidly. Although some studies have begun to focus on the time evolution of two-photon-atom interactions and have conducted preliminary discussions on the transient behavior of EIT systems, most of the work still solves the EIT driving equation under the steady-state assumption and pays insufficient attention to the complete response process of atoms to the external electric field. In order to further fill this research gap, we formulate a density-matrix model for a ladder-type three-level Rydberg system and solve the EIT-driven equations under non-steady-state conditions. Numerical simulations reveal the real-time evolution of the atomic response during two-photon excitation and elucidate how various system parameters shape this response. On this basis, we identify optimal parameter settings that enhance the real-time performance of Rydberg-atom quantum measurements and provide theoretical guidance for future sensor design.
Quantum sensing based on Rydberg atoms is an emerging technology for electric-field measurement. Theoretical and numerical studies were generally limited by the many-body effect in atomic ensembles. In this work, we initially derived a many-body dynamic equation by incorporating the Rydberg- Rydberg interaction into the four-level optical Bloch equation. Particularly, we proposed a fast steady-state solution as an alternative to the transient one. As a result, we ingeniously replaced the computationally expensive matrix operations with a linearly iterative process, enabling rapid convergence within few steps while considering the Doppler frequency shift. This approach made it possible to simulate the interaction of 7000 atoms in less than a minute. Based on the many-body model, we investigated the phenomenon of electromagnetically induced transparency (EIT) and Autler- Townes (AT) splitting under varying atomic gas densities; and compared the numerical results with experimental data. The comparison revealed a relatively-low error of 4.59% for the EITAT simulation by the many-body model. Moreover, we found that the linear dynamic range of the quantum sensing shrinks when considering the many-body interaction.
Over the past decade, Rydberg atom electric field sensors have been under investigation as potential alternatives or complements to conventional antenna-based receivers for select applications in RF communications, remote sensing, and precision metrology. To understand the potential utility of these devices for various use cases, it is crucial to develop models that accurately predict key performance metrics such as instantaneous bandwidth and dynamic range. However, existing numerical models require solving a large set of coupled differential equations that is computationally intensive and lengthy to solve. We present an analytic approach that can be used to derive an impulse response function that allows up to two orders-of-magnitude reduction in computation time compared to the full time-dependent integration of the equations of motion. This approach can be used to enable rapid assessments of the Rydberg sensor's response to various waveforms.
Abstract Rydberg atoms will produce the Stark effect under the action of non-resonant electric fields. Due to Rydberg atoms’ inherent energy level characteristics, they show sensitivity to electric fields and excellent self-calibration, which makes them promising in electric field measurement. In this paper, an experimental platform is established by fixing the probe and coupling laser frequencies. The ‘amplitude attenuation’ phenomenon of resonance point laser intensity oscillation caused by the change of electric field frequency is observed and analyzed, and its evolution trend is clarified; then, in different frequency bands (Hz band and kHz band), the density matrix equations are constructed and solved respectively in combination with the atomic energy level excitation structure, through which the dynamic response characteristics between atoms and AC electric fields are revealed. Finally, this paper proposes the Hz band electric field measurement method and the kHz band electric field measurement method: (1) in the steady-state solution of the electromagnetically induced transparency (EIT)-Stark mathematical model, the laser intensity curve at the resonance point laser intensity is inverted into an electric field waveform in real time to achieve Hz electric field measurement based on Rydberg atoms; (2) in the non-steady-state solution of the EIT-Stark mathematical model, the electric field amplitude is predicted by identifying the laser intensity amplitude and frequency at the laser intensity curve with the help of a neural network, thus achieving kHz electric field measurement based on Rydberg atoms. Experimental results show that the accuracy of the Hz band electric field measurement method proposed in this paper is greater than 99%, and the accuracy of the kHz band electric field measurement method is greater than 96%.
The quantum measurement of the microwave electric field based on Rydberg atoms developed in recent years has shown promise for enhancing accuracy, sensitivity and stability. However, the study of ultra-low frequency electric field measurements in power systems is still in its early stages, presenting new challenges for Rydberg-based measurement techniques. In this work, a ladder-type two-photon three-level structure of Cs atoms is selected, and the corresponding experimental system is constructed. Two kinds of laser control schemes, which are referred to as mismatch and match measurement schemes, are then proposed, and the quantum effect’s optical spectrum is obtained by using the two measurement schemes. After these measured spectral properties are compared, the match measurement scheme is chosen for real-time measurement of ultra-low frequency electric fields. Additionally, dynamic models of the interactions among the laser field, ultra-low frequency electric field and atoms are derived, on the basis of which theoretical simulations are being conducted to study the effects of the input parameters of the electric field and laser power on the optical spectrum. On the basis of the optical spectral features, an inversion method for the excitation electric field in real time is proposed, and its effectiveness is demonstrated.
We investigate the transient optical response property of an electromagnetically induced transparency (EIT) in a cold Rydberg atomic gas. We show that both the transient behavior and the steady-state EIT spectrum of the system depend strongly on Rydberg interaction. Especially, the response speed of the Rydberg-EIT can be five times faster (and even higher) than the conventional EIT without the Rydberg interaction. For comparison, two different theoretical approaches (i.e., two-atom model and many-atom model) are considered, revealing that Rydberg blockade effect plays a significant role for increasing the response speed of the Rydberg-EIT. The fast-responding Rydberg-EIT by using the strong, tunable Rydberg interaction uncovered here is not only helpful for enhancing the understanding of the many-body dynamics of Rydberg atoms but also useful for practical applications in quantum information processing by using Rydberg atoms.
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.