Realization of an inherent time crystal in a dissipative many-body system

Theoretical model

We investigate a system consisting of a collection of four-level atoms that are driven by a continuous-wave (CW) laser, as depicted in Fig. 1a, b. There are a pair of Kramers doublets for both the optical ground and excited states. The atoms possess electron spins and interact with one another via magnetic dipole-dipole interactions. The system Hamiltonian is the sum of the Hamiltonian of individual atoms, which is given by