\hat{b}^+_j\hat{a}^+_i\hat{a}^+_i\hat{a}_i=2\langle \hat{a}^+_i\hat{a}_i \rangle\hat{b}^+_j \hat{a}^+_i=2\langle \hat{a}^+_i\hat{a}_i \rangle\hat{a}^+_i\hat{b}^+_j