text: *t*′) + ˜*D*(1) 
  *kl*δ(*t*
  − 
  *t*′ + τ) + ˜*D*(3) 
  *kl*δ(*t*
  − 
  *t*′ + τ +*T*) + ˜*D*(5) 
  *kl*δ(*t*
  − 
  *t*′ + 2τ +*T*) + ˜*D*(7) 
  *kl*δ(*t*
  *t*′ +*T*), 
  *kl*δ(*t*
  *kl*δ(*t*
  *kl*δ(*t*
  *kl*δ(*t*
  *kl*δ(*t*
  
  τ  *t*′  *T*) 
  −  − 
  2τ  *t*′  *T*) 
  
  − 
  *t*′  − 
  *T*) 
  −  − 
  (8) 
  − 
  
  where ˜*D*(*i*) 
  related to quantum Langevin diﬀusion coeﬃcients*D*(*i*) 
  [27]. 
  *a*(*t*), 
  
  *Steady-state solutions:*The steady-state solutions for the 
  mean values of the ﬁeld and atomic variables for laser op- 
  eration are obtained by dropping the noise terms of the c- 
  number Langevin equations and setting the time derivatives 
  equal to zero. The analytical solutions are very complex, and 
  one could numerically solve the steady-state equations. In this 
  paper, we only care about the bad cavity limit γ*max*≪ 
  ≪ 
  τ− 
  κ/2. Since the atomic transit time is much shorter than 
  the damping times of atomic variables, one could ignore the 
  eﬀect of the spontaneous emission of the atom. By the stan- 
  dard way [25], We get the following steady-state values: 
  , 
  
  , 
  
  , 
  
  , 