{c}

<XY8> is an eight-pulse refocusing phase pattern whose nominal $\pi$ rotations follow
$$
X\;Y\;X\;Y\;Y\;X\;Y\;X.
$$
Here $X$ and $Y$ denote rotations about perpendicular axes of the <rotating frame>, not different flip angles. The pattern is used to reduce cumulative <NMR pulse errors> and is also used in broader spin-control experiments.<Experimental realization of robust dynamical decoupling with bounded controls in a solid-state spin system by F. Wang and others>[Accepted manuscript, p.2, Results: explicit XY8 order and Figure1]{ref}

The 1990 compensated-sequence paper compared x/y phase-alternating pulse trains experimentally and described compensation of errors affecting all three <magnetization> components, including applications to <REDOR>. The benefit concerns imperfect pulse trains: ideal rotations alone would not demonstrate that real pulse errors cancel.<New, compensated Carr-Purcell sequences by Terry Gullion and others>[Original Abstract: compensation, three magnetization components and applications]{ref}

For an original idealized check on a <magnetization> vector, a $\pi$ rotation about $x$ has matrix $R_x=\operatorname{diag}(1,-1,-1)$, while $R_y=\operatorname{diag}(-1,1,-1)$. Multiplying the eight matrices in the stated order gives the identity. All three vector components therefore return to their initial values if free evolution and pulse imperfections are omitted. This check verifies the ideal net action; it does not model the cancellation of imperfect rotations.

Three repeated <XY8> blocks contain24 refocusing pulses, before counting preparation and readout pulses. With instantaneous pulses separated by a centre-to-centre interval $\tau$ and half-interval end gaps, their ideal evolution window is $24\tau$. Finite pulse durations and the actual interaction being refocused must be included in a quantitative experiment.

<Jacob Schaefer>'s retrospective reports that applying <XY8> to <REDOR> reduced off-resonance amplitude and phase distortions in long pulse trains, enabling measurement of weak <NMR dipolar couplings>. That is a concrete experimental motivation for phase routing, rather than a claim that <XY8> removes every kind of noise.<Development of REDOR rotational-echo double-resonance NMR by Jacob Schaefer (2011)>[p.422, XY8 phase-routing discussion]{ref}


 XY8 (source code)