The evolution of (a) single-mode fluctuation and (b) two-mode fluctuation of the levitated nanospheres. In panel (a), Γ 0 = 2 ω m , d 0 = 0.5 ω m , and Ω CL = 2 ω m . In panel (b), for the green line, Γ 0 = 2 ω m and d 0 = 0.5 ω m ; for other dashed lines, γ i = γ 0 = 0 . We let Ω i = ω m .