Breakdown of Carr-Purcell Meiboom-Gill spin echoes in inhomogeneous fields

The Carr-Purcell Meiboom-Gill (CPMG) experiment has been used for decades to measure nuclear-spin transverse ($T_2$) relaxation times. In the presence of magnetic-field inhomogeneities, the limit of short interpulse spacings yields the intrinsic $T_2$ time. Here we show that the signal decay in such experiments exhibits fundamentally different behaviors between liquids and gases. In gases, CPMG unexpectedly fails to eliminate the inhomogeneous broadening due to the non-Fickian nature of the motional averaging.