Spin echo

Spin echo consists of applying a sequence of two magnetic pulses to an inhomogeneous spin assembly, as described below.
1) You first apply a pi/2 pulse, which puts the system in a superposition of states |-> and |+>.
2) Due to Larmor precession, the spin average value rotates around the vertical axis. However, due to a spatial inhomogeneity - for example in the applied B0 field - the Larmor frequency is not the same for all spins. Some of them (shown here in blue) precess more slowy than others (shown in red). Consequently, the total magnetization induced in the sample decays.
3) After a time delay T, a pi pulse is applied to the spin assembly. The resulting pi precession flips the spin in the equatorial plane. The faster spin are now behind the slower ones.
4) After an additional delay T, the faster spins catch up with the slower ones, resulting in a spin echo. This produces a peak in the total magnetization which can be experimentally measured despite the inhomogeneous spreading of Larmor frequencies.
5) Eventually the total magnetization decays again.

Note that this version is obsolete. Please see the new version.