Physics

Attractor

Mathematics

Parameter space

Noise (video)

Algorithm

Image (mathematics)

Statistical physics

Statistics

Phase transition

Mathematical analysis

Artificial intelligence

Chemistry

Oscillation (cell signaling)

Computer science

Quantum mechanics

State (computer science)

Biochemistry

Classical mechanics

Dissipative system

Nature

In many disciplines, states that emerge in open systems far from equilibrium are determined by a few global parameters 1,2 . These states can often mimic thermodynamic equilibrium, a classic example being the oscillation threshold of a laser 3 that resembles a phase transition in condensed matter. However, many classes of states cannot form spontaneously in dissipative systems, and this is the case for cavity solitons 2 that generally need to be induced by external perturbations, as in the case of optical memories 4,5 . In the past decade, these highly localized states have enabled important advancements in microresonator-based optical frequency combs 6,7 . However, the very advantages that make cavity solitons attractive for memories—their inability to form spontaneously from noise—have created fundamental challenges. As sources, microcombs require spontaneous and reliable initiation into a desired state that is intrinsically robust 8–20 . Here we show that the slow non-linearities of a free-running microresonator-filtered fibre laser 21 can transform temporal cavity solitons into the system’s dominant attractor. This phenomenon leads to reliable self-starting oscillation of microcavity solitons that are naturally robust to perturbations, recovering spontaneously even after complete disruption. These emerge repeatably and controllably into a large region of the global system parameter space in which specific states, highly stable over long timeframes, can be achieved.

Self-emergence of robust solitons in a microcavity