i´ve got a question concerning Ramsey interferometry and fringes. Consindering the case we have 2 pi/2 pulses as usual. For this case it is easy to calculate the mean value of the Bloch component w by applying a rotation matrix, say rotating around the Bloch component v. Then applying a rotation matrix around the axis w - our free precission. Finally, we apply again a roation matrix similar to the first one. From this we can conlcude the value for w. However, we have now an ensemble of atoms with different detuning which shows a gaussian distribution. How does one consider this in the calculation? I guess the gaussian distribution of the detuning affects our second matrix but I dont know how. If anyone has any suggestions or ideas how to tackle this problem, I would be very grateful! (my problem originates from a german exercise (5.3) if this may be helpful: http://www.quantum.physik.uni-mainz...__2006__ws0607_atomphysik__Uebungsblatt05.pdf) Cheers!