Steady states of Λ-type three-level systems excited by quantum light with various photon statistics in lossy cavities

<jats:title>Abstract</jats:title> <jats:p>The interaction between quantum light and matter is being intensively studied for systems that are enclosed in high-<jats:italic>Q</jats:italic> cavities which strongly enhance the light–matter coupling. Cavities with low <jats:italic>Q</jats:italic>-factors are generally given less attention due to their high losses that quickly destroy quantum systems. However, bad cavities can be utilized for several applications, where lower <jats:italic>Q</jats:italic>-factors are required, e.g., to increase the spectral width of the cavity mode. In this work, we demonstrate that low-<jats:italic>Q</jats:italic> cavities can be beneficial for preparing specific electronic steady states when certain quantum states of light are applied. We investigate the interaction between quantum light with various statistics and matter represented by a Λ-type three-level system in lossy cavities, assuming that cavity losses are the dominant loss mechanism. We show that cavity losses lead to non-trivial electronic steady states that can be controlled by the loss rate and the initial statistics of the quantum fields. We discuss the mechanism of the formation of such steady states on the basis of the equations of motion and present both analytical expressions and numerical simulations for such steady states.</jats:p>