Spontaneous emergence of temporal structures in a continuously driven many-body system

The spontaneous emergence of temporal structures challenges the conventional understanding that systems governed by time-invariant laws remain unchanged over time. Recent experiments have observed this time translation symmetry breaking in quantum atomic systems that either exhibit strong atom-atom interactions or have low dissipation rates. While current theoretical frameworks reveal the importance of strong atom-atom interactions, they fall short in explaining this phenomenon observed in low-dissipation atomic systems. Here, we present a theoretical study on the spontaneous breaking of time translation symmetry in materials with low dissipation rates. By constructing phase diagrams for a system of four-level atoms driven by a continuous-wave optical field, we identify the essential requirements for self-sustained temporal motions. These include a driven open system, nonlinear interactions, and sufficient degrees of freedom that facilitate competing processes. Our findings contribute to a better understanding of the emergence of spontaneous time translation symmetry breaking in these materials.