Figure 1

Model: The three optomechanical cavities can be coupled either (a) reversibly via coherent photon exchange (tunneling) between nearest neighbors or (b) irreversibly as forward feed using circulators. The array exhibits a different topology for each coupling configuration.Reuse & Permissions

Figure 2

Reversible coupling with the full interaction. The temporal evolution of the entanglement, $E_N$, quantified by the logarithmic negativity between all possible selections of intercavity modes of the optomechanical array: (a) phonon-phonon and (b) photon-phonon, where we have chosen ${\kappa }_{1,2,3}=\kappa$, ${\mu }_{1,2,3}/\kappa =0.01$, ${\Delta }_{1,2,3}/\kappa ={\omega }_{1,2,3}/\kappa =200$, $g_{1,2,3}/\kappa =0.5$, ${\chi }_{12}/\kappa ={\chi }_{23}/\kappa =1$, and $\overline{n}=0$.Reuse & Permissions

Figure 3

Reversible coupling with the full interaction. The temporal evolution of the entanglement, $E_N$, quantified by the logarithmic negativity between intercavity phonon modes $b_1,b_2$ of the optomechanical array as a function of (a) detuning of cavity 1, ${\Delta }_1$, and (b) thermal occupation number $\overline{n}$, where we have chosen ${\kappa }_{1,2,3}=\kappa$, ${\mu }_{1,2,3}/\kappa =0.01$, ${\omega }_1/\kappa =200$, ${\Delta }_{2,3}/\kappa ={\omega }_{2,3}/\kappa =200$, $g_{1,2,3}/\kappa =0.5$, and ${\chi }_{12}/\kappa ={\chi }_{23}/\kappa =1$.Reuse & Permissions

Figure 4

Reversible coupling with cavity 1 blue detuned and cavity 2 red detuned. The temporal evolution of entanglement, $E_N$, quantified by the logarithmic negativity between the intercavity phonons of two optomechanical cavities ($b_1$,$b_2$), where we have chosen ${\kappa }_{1,2}=\kappa$, ${\mu }_{1,2}/\kappa =0.01$, $g_1/\kappa =0.02$, and ${\chi }_{12}/\kappa =1$, (a) with $\overline{n}=0$ and different $g_2/\kappa$: 0.1 (solid line), 0.2 (dashed line), 0.3 (dashed dotted line), and 0.4 (dotted line), and (b) as a function of thermal phonon number $\overline{n}$ with $g_2/\kappa =0.1$.Reuse & Permissions

Figure 5

Reversible coupling with cavity 1 blue detuned and cavity 2 red detuned. The steady-state entanglement $E_N$ quantified by the logarithmic negativity between the intercavity phonons of two optomechanical cavities ($b_1$,$b_2$), where we have chosen ${\kappa }_{1,2}=\kappa$, ${\mu }_{1,2}/\kappa =0.01$ and $\overline{n}=0$, (a) as a function of $g_1/\kappa$ and $g_2/\kappa$ for ${\chi }_{12}/\kappa =1$, and (b) as a function of $g_2/\kappa$ for $g_1=0.02$ and different ${\chi }_{12}/\kappa$: 1 (solid line), 0.5 (dashed line), and 0.2 (dotted line). The inset shows the correlation $\langle a_1{a}_2^{†}\rangle$ as a function of $g_2/\kappa$ for the same parameters, except for ${\chi }_{12}/\kappa =1$ and $g_1/\kappa =0.02$.Reuse & Permissions

Figure 6

Forward feed coupling with the full interaction. The temporal evolution of the entanglement, $E_N$, quantified by the logarithmic negativity between all possible intercavity modes of the optomechanical array: (a) phonon-phonon and (b) photon-phonon, where we have chosen ${\kappa }_{1,2,3}=\kappa$, ${\mu }_{1,2,3}/\kappa =0.01$, ${\Delta }_{1,2,3}/\kappa ={\omega }_{1,2,3}/\kappa =400$, $g_{1,2,3}/\kappa =0.5$, and $\overline{n}=0$.Reuse & Permissions

Figure 7

Forward feed coupling with the full interaction. The temporal entanglement $E_N$ quantified by the logarithmic negativity between intercavity phonons $b_1,b_2$ of the optomechanical array as a function of (a) detuning of cavity 1, ${\Delta }_1$, and (b) thermal occupation number $\overline{n}$, where we have chosen ${\kappa }_{1,2,3}=\kappa$, ${\mu }_{1,2,3}/\kappa =0.01$, ${\omega }_1/\kappa =400$, ${\Delta }_{2,3}/\kappa ={\omega }_{2,3}/\kappa =400$, $g_{1,2,3}/\kappa =0.5$, and $\overline{n}=0$.Reuse & Permissions

Figure 8

Forward feed coupling with cavity 1 blue detuned and cavity 2 red detuned. The temporal evolution of entanglement, $E_N$, quantified by the logarithmic negativity between the intercavity phonons of two optomechanical cavities ($b_1$,$b_2$), where we have chosen ${\kappa }_{1,2}=\kappa$, ${\mu }_{1,2}/\kappa =0.01$, $g_1/\kappa =0.02$, (a) with $\overline{n}=0$ and different $g_2/\kappa$: 0.1 (solid line), 0.2 (dashed line), 0.3 (dashed dotted line), and 0.4 (dotted line), and (b) as a function of thermal phonon number $\overline{n}$ with $g_2/\kappa =0.1$.Reuse & Permissions

Figure 9

Forward feed coupling with cavity 1 blue detuned and cavity 2 red detuned. (a) The steady-state entanglement $E_N$ quantified by the logarithmic negativity between the intercavity phonons of two optomechanical units ($b_1$,$b_2$) vs $g_1/\kappa$ and $g_2/\kappa$, where we have chosen ${\kappa }_{1,2}=\kappa$, ${\mu }_{1,2}/\kappa =0.01,$ and $\overline{n}=0$. (b) The steady-state correlation $\langle a_1{a}_2^{†}\rangle$ as a function of $g_2/\kappa$ with the same parameters but with $g_1/\kappa =0.02$.Reuse & Permissions