 \frac{d\alpha_{0}}{dt} & = & -(\gamma_{a}+i\Delta_{a})\alpha_{0}+\kappa\alpha_{0}^{+}\beta_{0}+iJ_{a}\alpha_{0}+\sqrt{\kappa\beta_{0}}\;\eta_{0}(t),\nonumber \\ \frac{d\alpha_{0}^{+}}{dt} & = & -(\gamma_{a}-i\Delta_{a})\alpha_{0}^{+}+\kappa\alpha_{0}\beta_{0}^{+}-iJ_{a}\alpha_{0}^{+}+ \sqrt{\kappa\beta_{0}^{+}}\;\eta_{0}(t),\nonumber \\ \frac{d\alpha_{0}}{dt} & = & -(\gamma_{a}+i\Delta_{a})\alpha_{0}+\kappa\alpha_{0}^{+}\beta_{0}+iJ_{a}\alpha_{0}+\sqrt{\kappa\beta_{0}}\;\eta_{0}(t),\nonumber \\ \frac{d\alpha_{0}^{+}}{dt} & = & -(\gamma_{a}-i\Delta_{a})\alpha_{0}^{+}+\kappa\alpha_{0}\beta_{0}^{+}-iJ_{a}\alpha_{0}^{+}+ \sqrt{\kappa\beta_{0}^{+}}\;\eta_{0}(t),\nonumber \\ \frac{d\beta_{0}}{dt} & = & \epsilon_{0}-(\gamma_{b}+i\Delta_{b})\beta_{0}-\frac{\kappa}{0}\alpha_{0}^{0}+iJ_{b}\beta_{0},\nonumber \\ \frac{d\beta_{0}^{+}}{dt} & = & \epsilon_{0}^{\ast}-(\gamma_{b}-i\Delta_{b})\beta_{0}^{+}-\frac{\kappa}{0}\alpha_{0}^{+\;0}-iJ_{b}\beta_{0}^{+},\nonumber \\ \frac{d\beta_{0}}{dt} & = & \epsilon_{0}-(\gamma_{b}+i\Delta_{b})\beta_{0}-\frac{\kappa}{0}\alpha_{0}^{0}+iJ_{b}\beta_{0},\nonumber \\ \frac{d\beta_{0}^{+}}{dt} & = & \epsilon_{0}^{\ast}-(\gamma_{b}-i\Delta_{b})\beta_{0}^{+}-\frac{\kappa}{0}\alpha_{0}^{+\;0}-iJ_{b}\beta_{0}^{+},