  In attempts to unify the four known fundamental forces in a single
quantum-consistent theory, it is suggested that Lorentz symmetry may be broken
at the Planck scale. Here we search for Lorentz violation at the low-energy
limit by comparing orthogonally oriented atomic orbitals in a
Michelson-Morley-type experiment. We apply a robust radiofrequency composite
pulse sequence in the $^2F_{7/2}$ manifold of an Yb$^+$ ion, extending the
coherence time from 200 $\mu$s to more than 1 s. In this manner, we fully
exploit the high intrinsic susceptibility of the $^2F_{7/2}$ state and take
advantage of its exceptionally long lifetime. We match the stability of the
previous best Lorentz symmetry test nearly an order of magnitude faster and
improve the constraints on the symmetry breaking coefficients to the 10$^{-21}$
level. These results represent the most stringent test of this type of Lorentz
violation. The demonstrated method can be further extended to ion Coulomb
crystals.
