Robust bilinear rotations

Bilinear rotation elements allow interaction-dependent manipulations of spins in quantum technologies and, particularly, in spectroscopy. We used bilinear rotation in nuclear magnetic resonance (NMR) spectroscopy and derived several ways of introducing robustness into the filter element. We distinguished two performance levels: the coupling dependent inversion of polarization and the full bilinear π-rotation capability. In addition, all four essential variants of bilinear π rotations-BIRD<i>^d</i>, BIRD<i>^r</i>, BIRD^{<i>d</i>,<i>X</i>}, and BIRD^{<i>r</i>,<i>X</i>} filters-were given for all cases studied. In the first step, adiabatic CHIRP-type and BUBI/BUBU pulses lead to improved robustness with respect to offset/detuning effects and variations in <i>B</i>₁-field strengths. In the second step, we optimized time-optimal coupling-compensated BIRD elements. Together with correspondingly optimized pulse shapes, we established fully coupling, offset, and <i>B</i>₁-compensated bilinear π-rotation (COB-BIRD) elements and characterized them in theory and experiment. Overall, this demonstrated the use of the robust bilinear rotation capability on a partially aligned sample in a homodecoupled two-dimensional NMR experiment.