We use photoluminescence spectroscopy of bright and dark exciton states in single InP/GaInP quantum dots to measure hyperfine interaction of the valence band hole with nuclear spins polarized along the sample growth axis. The ratio of the hyperfine constants for the hole (C) and electron (A) is found to be C/A~-0.11. In InP dots the contribution of spin 1/2 phosphorus nuclei to the hole-nuclear interaction is weak, which enables us to determine experimentally the value of C for spin 9/2 indium nuclei as C_In~-5 micro-eV. This high value of C is in good agreement with recent theoretical predictions and suggests that the hole-nuclear spin interaction has to be taken into account when considering spin qubits based on holes.
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