Spin Inversion and the Adiabatic Theorem

Inversion pulses are very important because of the wide variety of applications in experiments involving coherence selection and spin decoupling. One of the very first methods for spin inversion was the rapid adiabatic passage introduced by Bloch [18]. 

According to the adiabatic theorem [19,20], if the change of direction of the magnetic field is sufficiently slow, the angle between the magnetization M and the instantaneous direction of the effective field (ooeff) is a constant of motion. The adiabatic condition for spin inversion is given by equations (6) and (7)  

The second criterion (equation (7)) implies that the adiabatic sweep starts and ends with the effective field aligned with the z axis. The degree to which the adiabatic condition is satisfied can be quantified by introducing the factor of adiabacity (Q)  

From equation (8) three modes of adiabatic spin inversion using RF pulses may be defined as (a) amplitude modulated pulses, e.g. I-BURP [13], G3[16], I-SNOB [17], (b) frequency modulated pulses, e.g. chirp [18,20], tangential sweep [20,21] and (c) both amplitude and frequency modulated pulses, e.g. the hyperbolic secant [22] or WURST (Wide band Uniform Rate Smooth Truncation) [23] pulse. 

---