Single-Atom Microwave Amplification Assisted by Multi-Rabi Sideband Interference in a 1D Waveguide QED System

To achieve precise measurements, an efficient signal amplifier is essential to enhance the intensity of the probe signal, especially in noisy environments. However, developing such an amplifier in a three-dimensional setup-where a single atom interacts with the continuous modes of three-dimensional electromagnetic fields-presents challenges due to spatial mode mismatches, resulting in weak coupling.  A viable solution is to confine the electromagnetic fields within a one-dimensional environment. In this study, we explore microwave amplification achieved by a single superconducting multi-level atom, specifically a transmon, driven by a strong pump field through the continuous modes of a semi-infinite one-dimensional waveguide.  The atom can be excited to a higher energy state through a multi-photon process, leading to the generation of multiple dressed states. Our theoretical investigation focuses on the amplification mechanism triggered by stimulated emission from nearly degenerate dressed states, taking into account the effects of quantum interference.