EIT A Resonance Perspective

To utilize the adiabatic condition, we transform H to a form that does not contain oscillatory terms that might cause rapid variations of dU/dt and hence invalidate tti S 

Having removed the oscillatory e iAl terms, we now build adiabatic solutions by diagonalizing Eq. (9.34) [as in Eq. (9.10)] to obtain a 2 x 2 unitary eigenvector matrix  

Operating with on Eq. (9.33), defining a = nt Cs(a] a2) and neglecting /dt, we obtain an equation analogous to Eq. (9.13) for a, with H replacing H e solutions to this equation in the adiabatic approximation are 

Vp lhow introduce the (weak) l t) pulse. Since IE)) is the initially populated jiqither the IE)) or E2) states, nor the )A1) and 12) adiabatic states, can ever be filed in the absence of ](t). Therefore, in the absence of the x(t) pulse, the jpticeable effect of 2(t) is to change the spectrum of the Hamiltonian. Assum-.2 the adiabatic condition [Eq. (9.40)] indeed holds, the states seen by the , (t) 

Thus the time evolution of the [E0) component of Aj(f)) is governed by a q-energy of E0 — Q2(f), whereas the time evolution of the / 0) component of is governed by a quasi-energy ofE0 + [02(r).  

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