By perturbative expansion Initial state √2 个)+) B(t) Probability to state t+)5 P(a)=-(1+cos(a-4dpo) 0(a)The field is (instantaneously) prepared at its initial value, which is at angle theta to the Z axis. at the same time the spin is (instantaneously) placed in the above initial state (b) we adiabatically rotate the magnetic field clockwise n times around a closed loop (c)the spin is flipped and (d)the field is rotated anticlockwise, the same times n (e) the spin is flipped again and (f the spin state is measured H=-g()+∑92(bb+12)-∑h202的+b)17 By perturbative expansion B(t)  1 (| | ) 2 +  Initial state (a) The field is (instantaneously) prepared at its initial value, which is at angle theta to the z axis. At the same time the spin is (instantaneously) placed in the above initial state (b) we adiabatically rotate the magnetic field clockwise, n times around a closed loop (c) the spin is flipped and (d) the field is rotated anticlockwise, the same times n . (e) the spin is flipped again and (f) the spin state is measured. Probability to state 1 / 2 / 2 ( | | ) 2 i i e e   −  +  is 0 1 ( ) (1 cos( 4 )) 2 P   = + −  , , , , , , , ( ) ( 1/ 2) ( ) j j j j j j j j H gB t b b h b b           + + = − +  + − +  