Fig. 4: Robustness of the atom-mechanical entanglement.

a Logarithmic negativity for the full (solid curves) solution depending on the coupling (assuming \(G=g\)). Here, \(\eta =1\), \({\gamma }_{{\mathrm {m}}}=1{0}^{-5}{\kappa }_{{\mathrm {m}}}\), \(S=5\) dB, mechanical rethermalization rate \({\Gamma }_{{\mathrm {m}}}=1{0}^{-3}{\kappa }_{{\mathrm {m}}}\), initial mechanical occupation \({n}_{0}=0\) for the different values of \(\tau {\kappa }_{{\mathrm {m}}}\). Dashed curves of the corresponding colors demonstrate the adiabatic solution with these parameters. b Logarithmic negativity for the full solution depending on a mechanical rethermalization rate \({\Gamma }_{{\mathrm {m}}}\) calculated for two cases of coupling rates using different initial mechanical occupation \({n}_{0}\). Here, \(\eta =1\), \({\gamma }_{{\mathrm {m}}}=1{0}^{-5}{\kappa }_{{\mathrm {m}}}\), \(S=5\) dB, and \(\tau {\kappa }_{{\mathrm {m}}}=100\). The inset is the \(y\)-scale zoom of the main figure.