<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>

<jats:title>Abstract</jats:title><jats:p>Semiconductor quantum dots are excellent candidates for ultrafast coherent manipulation of qubits by laser pulses on picosecond timescales or even faster. In inhomogeneous ensembles a macroscopic optical polarization decays rapidly due to dephasing, which, however, is reversible in photon echoes carrying complete information about the coherent ensemble dynamics. Control of the echo emission time is mandatory for applications. Here, we propose a concept to reach this goal. In a two-pulse photon echo sequence, we apply an additional resonant control pulse with multiple of 2<jats:italic>π</jats:italic> area. Depending on its arrival time, the control slows down dephasing or rephasing of the exciton ensemble during its action. We demonstrate for self-assembled (In,Ga)As quantum dots that the photon echo emission time can be retarded or advanced by up to 5 ps relative to its nominal appearance time without control. This versatile protocol may be used to obtain significantly longer temporal shifts for suitably tailored control pulses.</jats:p>