Fig. 2: Results of the simulations.

Results of stroboscopic application of cubic nonlinear potential V = γx³/(6τ) to the squeezed thermal state (initial occupation n₀ = 0.05, squeezing s = 1.2) over multiple (M_T = 1, 2, or 3) halves of mechanical periods. a Squeezing of nonlinear quadrature. Thick lines correspond to stroboscopic method with realistic parameters and thermal noise, thin lines, to purely unitary application of the nonlinearity. Dashed lines correspond to the result of evolution driven by the full Hamiltonian \(\hat{H}\) (1) from the same initial state over time τ, 2τ, and 3τ respectively. b Wigner function of motional states. Solid lines correspond to the same states from (a). Cyan line with markers (overlapping with solid red line) shows the unitary application of nonlinearity. Other parameters are as follows: potential stiffness γ = γ₀ = 0.2, application duration τΩ_m = Θ = Θ₀ = π/100, environmental thermal heating rate parameter H₀ = 4πH_m/Ω_m = 0.002.