# A Ramsey fringes - free oscillations

Tags:
1. Feb 8, 2017

### OnestoneFringe

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!