Fast simulation for interacting four-level Rydberg atoms: electromagnetically induced transparency and Autler-Townes splitting.

Quantum sensing using Rydberg atoms is an emerging technology for precise measurement of electric fields. However, most existing computational methods are all based on a single-particle model and neglect Rydberg-Rydberg interaction between atoms. In this study, we introduce the interaction term into the conventional four-level optical Bloch equations. By incorporating fast iterations and solving for the steady-state solution efficiently, we avoid the computation of a massive 4N × 4N dimensional matrix. Additionally, we apply the Doppler frequency shift to each atom used in the calculation, eliminating the requirement for an additional Doppler iteration. These schemes allow for the calculation of the interaction between 7000 atoms around one minute. Based on the many-body model, we investigate the Rydberg-Rydberg interaction of Rydberg atoms under different atomic densities. Furthermore, we compare our results with the literature data of a three-level system and the experimental results of our own four-level system. The results demonstrate the validity of our model, with an effective error of 4.59% compared to the experimental data. Finally, we discover that the many-body model better predicts the linear range for measuring electric fields than the single-particle model, making it highly applicable in precise electric field measurements.

Electrodynamic modeling of threshold-free lasing in photonic time crystals.

An electrodynamic model is presented in this Letter to describe thresholdless lasers, utilizing the application of photonic time crystals (PTCs). By integrating the distinctive physical properties of PTCs and employing a comprehensive model based on a four-level system, the feasibility of achieving thresholdless laser operation is demonstrated. The proposed electrodynamic model comprehensively captures the intricate interplay between the electromagnetic field and the PTC medium. The model takes into account the ultrafast periodic variations in the refractive index of the PTCs, which arise from their time crystal-like behavior. Additionally, the dynamic response of the four-level system is considered, factoring in the processes of population inversion and relaxation. This Letter seeks to elucidate the underlying mechanisms that facilitate thresholdless laser operation in PTC-based systems. Through our electrodynamic modeling approach, we demonstrate that the ultrafast variations in the refractive index of PTCs give rise to a self-sustaining laser action, obviating the need for a lasing threshold. Moreover, we investigate the impact of various parameters, including pump power and modulation period, on the laser's performance and output characteristics. The developed electrodynamic model provides a comprehensive framework for comprehending and designing thresholdless lasers based on photonic time crystals. This research contributes to the advancement of thresholdless laser technology and opens up possibilities for applications in optical communications, sensing, and quantum photonics.

Auxiliary differential equation (ADE) method based complying-divergence implicit FDTD method for simulating the general dispersive anisotropic material.

The preceding works introduced the leapfrog complying divergence implicit finite-difference time-domain (CDI-FDTD) method, which exhibits high accuracy and unconditional stability. In this study, the method is reformulated to simulate general electrically anisotropic and dispersive media. The auxiliary differential equation (ADE) method is employed to solve the equivalent polarization currents, which are then integrated into the CDI-FDTD method. The iterative formulae are presented, and the calculation method is similar to that of the traditional CDI-FDTD method. Additionally, the Von Neumann method is utilized to analyze the unconditional stability of the proposed method. To evaluate the performance of the proposed method, three numerical cases are conducted. These include calculating the transmission and reflection coefficients of a monolayer graphene sheet and a monolayer magnetized plasma, as well as the scattering properties of a cubic block plasma. The numerical results obtained by the proposed method demonstrate its accuracy and efficiency in simulating general anisotropic dispersive media, compared to both the analytical method and the traditional FDTD method.

First-principle calculation of Chern number in gyrotropic photonic crystals.

As an important figure of merit for characterizing the quantized collective behaviors of the wavefunction, Chern number is the topological invariant of quantum Hall insulators. Chern number also identifies the topological properties of the photonic topological insulators (PTIs), thus it is of crucial importance in PTI design. In this paper, we develop a first principle computatioal method for the Chern number of 2D gyrotropic photonic crystals (PCs), starting from the Maxwell's equations. Firstly, we solve the Hermitian generalized eigenvalue equation reformulated from the Maxwell's equations by using the full-wave finite-difference frequency-domain (FDFD) method. Then the Chern number is obtained by calculating the integral of Berry curvature over the first Brillouin zone. Numerical examples of both transverse-electric (TE) and transverse-magnetic (TM) modes are demonstrated, where convergent Chern numbers can be obtained using rather coarse grids, thus validating the efficiency and accuracy of the proposed method.