  We experimentally study the breakdown of hyperfine coupling for an atom in a
deep optical-dipole trap. One-color laser spectroscopy is performed at the
resonance lines of a single $^{87}$Rb atom for a trap wavelength of 1064 nm.
Evidence of hyperfine breakdown comes from three observations, namely a
nonlinear dependence of the transition frequencies on the trap intensity, a
splitting of lines which are degenerate for small intensities, and the ability
to drive transitions which would be forbidden by selection rules in the absence
of hyperfine breakdown. From the data, we infer the hyperfine interval of the
$5P_{1/2}$ state and the scalar and tensor polarizabilities for the $5P_{3/2}$
state.
