Twin Limit Cycle Realized With Trapped Ions

Sideband cooling and heating on different ion transitions, see Fig. 10.14.
The video has two time scales t∈[0,1001] and t∈[1001,10000].

Preliminary data showing that a multi-limit-cycle oscillator can be realized by the nonlinear phonon-ion interaction described in Eq. (10.6.1). The parameters are s_BSB = -s_RSB = 1, Ω₀^BSB = Ω₀^RSB = 0.1κ, η_BSB = 0.8, and η_RSB = 0.9. (a) Wigner function and marginals of the final state of a time evolution of duration κt = 1000 starting from a coherent state |α=2 ⟩. (b) Populations ρ_n,n of the final state. The curves correspond to the heating Ω^BSB_n,n+1 and cooling Ω^RSB_n,n-1 sidebands, see Eq. (10.6.1). Populations of Fock numbers n≥19 are smaller than 10^-4.