  Using lowest-order lattice NRQCD to create heavy meson propagators and
applying the spin-dependent interaction, $c_B^{}
\frac{-g}{2m_q}\vec\sigma\cdot\vec{B}$, at varying intermediate time slices, we
compute the off-diagonal matrix element of the Hamiltonian for the
quarkonium-hybrid two-state system. Thus far, we have results for one set of
quenched lattices with an interpolation in quark mass to match the bottomonium
spectrum. After diagonalization of the two-state Hamiltonian, we find the
ground state of the $\Upsilon$ to show a $0.0035(1)c_B^2$ (with $c_B^2 \sim
1.5-3.1$) probability admixture of hybrid, $|b\bar{b}g>$.
