text: with frequency ω*j*
  )*j*is the “spin- 
  | 
  ﬂip” operator for the jth atom, with its adjoint σ*j*
  )*j*. 
  *a*
  | 
  | 
  The coupling constant*g*is given by*g*= µ √ω/2~ǫ0*V*, where 
  µ is the magnitude of the atomic dipole moment, and*V*is the 
  eﬀective volume of the cavity. 
  
  *a*and ω*j*
  *b*, and σ*j*
  = (  *b*
  *a*
  i h  |  − 
  + = ( 
  *b*
  i h 
  
  In order to denote the ﬁnite-time interaction between the 
  atoms and Ramsey separated ﬁeld, we introduce the function 
  
  Γ*j*(*t*) = Θ(*t* Θ(*t* τ)+Θ(*t* Θ(*t*
  
  *T*), 
  (2) 
  where Θ(*t*) is the Heaviside step function [Θ(*t*) = 1 for*t*> 0, 
  Θ(*t*) = 1/2 for*t*= 0, and Θ(*t*) = 0 for*t*< 0].*T*is the free 
  drift time of the atoms, and τ is the interacting time between 
  the atom and one cavity. 
  
  τ  2τ  *t j*) 
  *t j*−  *t j*− 
  *T*) 
  *t j*−  −  −  −  −  −  −  −  − 