Precise control of atom-light interactions is vital to many quantum information protocols. In particular, atomic systems can be used to slow and store light to form a quantum memory. Optical storage can be achieved via stopped light, where no optical energy remains in the atoms, or as stationary light, where some optical energy remains present during storage. In this work, we demonstrate a form of self-stabilising stationary light. From any initial state, our atom-light system evolves to a stable configuration that is devoid of coherent emission from the atoms, yet may contain bright optical excitation. This phenomenon is verified experimentally in a cloud of cold Rb87 atoms. The spinwave in our atomic cloud is imaged from the side allowing direct comparison with theoretical predictions.Coherent atom light interactions lie at the heart of many quantum information systems [1, 2]. In particular, implementations of quantum repeaters will likely rely on mapping of photonic states onto atomic systems to enable storage of quantum information [3,4]. Deterministic quantum logic gates in optical systems may also rely on atomic state mapping to enable nonlinear photon-photon interactions [5,6,7,8,9]. A fundamental issue facing any attempt to implement nonlinear cross phase modulation (XPM) is that the interaction is inherently very weak. Techniques are therefore required to increase the interaction time or interaction strength to allow useful amounts of phase shift. Interaction strength can be scaled up by choosing a nonlinear medium with strong optical interactions, such as Rydberg atoms [10,11]. A more general approach that works for any medium is to use smaller interaction volumes, since this increases the electric field per photon, and longer interaction times, which may be achieved by using an 1 arXiv:1609.08287v1 [quant-ph]