Fig. 3: From strong ME to weak ME.
a Logarithmic scale of distance \({{{\mathcal{D}}}}(\rho,{\rho }_{ss})\) evolves with time for different initial state: \(\left\vert 0\right\rangle\) (blue), \(\left\vert 2\right\rangle\) (green) and \(\left\vert {{{\rm{sME}}}}\right\rangle\) (red), respectively. b The corresponding coefficients c1(t) (of initial state \(\left\vert 0(2)\right\rangle\)) and c2(t) (of initial state \(\left\vert {{{\rm{sME}}}}\right\rangle\)). The sME that exits exponential acceleration is observed for Ω2/Ω1  =  0.04, 0.16( < LEP). When Ω2/Ω1  =  0.25( > LEP), \(\left\vert {{{\rm{sME}}}}\right\rangle\) has the same decay rate with the normal initial states \(\left\vert 0(2)\right\rangle\), meaning the strong ME disappears but weak ME is allowed. c Real parts of the eigenvalues of the Liouvillian operator as a function of Ω2/Ω1. d Overlaps ∣c1∣ (solid) and ∣c2∣ (dashed) for different initial states \(\left\vert 0\right\rangle\) (red) and \(\left\vert 2\right\rangle\) (green), respectively. The parameters are Ω1  =  2π  ×  20  kHz, κ1  =  2Ω1, κ2  =  0.0015Ω1. All error bars in this figure are calculated by using Monte Carlo simulation.
