Accelerating the analysis of optical quantum systems using the Koopman operator

Abstract: The prediction of photon echoes is a crucial technique for understanding optical quantum systems. However, it typically requires numerous simulations with varying parameters and input pulses, rendering numerical studies computationally expensive. This article investigates the use of data-driven surrogate models based on the Koopman operator to accelerate this process while maintaining accuracy over many time steps. To this end, we employ a bilinear Koopman model using extended dynamic mode decomposition to simulate the optical Bloch equations for an ensemble of inhomogeneously broadened two-level systems. These systems are well suited to describe the excitation of excitonic resonances in semiconductor nanostructures, such as ensembles of semiconductor quantum dots. We conduct a detailed study to determine the number of system simulations required for the resulting data-driven Koopman model to achieve sufficient accuracy across a wide range of parameter settings. We analyze the L2 error and the relative error of the photon echo peak and investigate how the control positions relate to stabilization. After proper training, our methods can predict the dynamics of the quantum ensemble accurately and with numerical efficiency.