\begin{aligned} \label{61a} \nonumber \\ \label{61a} a=\frac{\beta}{\sqrt{2\overline{\omega}\hbar}}\left[\left(g-i\overline{\omega}\right)r+y\right], \\ \label{41b} a^{\dagger}=\frac{\beta^{*}}{\sqrt{2\overline{\omega}\hbar}}\left[\left(g+i\overline{\omega}\right)r+y\right],\\ \end{aligned}