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.PACS numbers: 42.50. Hz, 32.60.+i, 32.10.Dk, 37.30.+i Optical dipole traps (ODTs), including optical lattices, are established tools for trapping cold atoms. They rely on a position-dependent light shift of the atomic ground state. Excited states usually change differently so that transition lines are shifted. The line shifts can be small, like in shallow traps, or even vanish, like in magic-wavelength traps [1,2]. However, magic wavelengths cannot always be employed because either the spontaneous emission rate would be too high, or highpower lasers are not available, or more than two atomic levels are used, making it impossible to find a wavelength that is simultaneously magic for all transitions. Nevertheless, the increasing demand for improved control of atoms makes it desirable to work in deep ODTs. The advantages of deep ODTs include precise localization of the trapped atoms, the possibility to perform resolvedsideband Raman cooling, and reduced atom loss in the presence of heating processes.Driving resonant transitions in deep ODTs requires precise knowledge of the atomic light shifts. For optical transitions, the excited-state light shifts are nontrivial and, interestingly, investigations on this subject are only at a beginning, although deep ODTs have long been employed in the fields of atomic clocks, quantum information processing (QIP), and quantum many-body physics. Examples include single-atom optical tweezers [3][4][5][6][7], atoms inside high-finesse cavities [8], atoms trapped close to nanophotonic waveguides [9] or resonators [10], atoms in hollow optical fibers [11], and quantum gas microscopes [12,13]. Line shifts might also become relevant in future experiments with ions in ODTs [14,15] and molecules in ODTs [16,17].Here we show that the differential light shifts depend nonlinearly on intensity for high intensities, in contrast to the well-known linear dependence for low intensities. The typical ODT depth, for which the nonlinear effect becomes comparable to the natural atomic linewidth is remarkably small, namely, k B × 0.4 mK for the parameters of our experiment, where k B is the Boltzmann constant. Moreover, we observe a splitting of resonances which * stephan.ritter@mpq.mpg.de would be degenerate in the linear regime and we observe a resonance which would be dipole forbidden in the linear regime. The data are ob...