Time crystals in levitated systems

The time crystal was proposed in 2012, and got a lot of attentions and disscussions. In 2017, discrete time crystal, which appeared in Floquet driving systems, was realized in time crystal. In this talk, I discuss the concept of time crystal and discrete time crystal, and briefly summarized our proposal of space-time crystal and time quasi-crystal in trapped ions systems. Inspired by this proposal, we find that the nearly spontaneous dynamics appears near the ground state of Lipkin-Meshkov-Glick (LMG) model with a finite number of spins. We link this phenomena to quantum time crystal and time quasicrystal. Finally, we propose a scheme to realize an effective classical time crystal in an optically levitated charged nanoparticle under a modest magnetic field. The Hamiltonian of the system is solved, and we find that the time crystal phenomena can appear near the ground state. The experimental feasibility is briefly discussed.