We report on the direct measurement of the electron spin splitting and the accompanying nuclear Overhauser (OH) field, and thus the underlying nuclear spin polarization (NSP) and fluctuation bandwidth, in a single InAs quantum dot under resonant excitation conditions with unprecedented spectral resolution. The electron spin splitting is measured directly via resonant spin-flip single photon Raman scattering detected by superconducting nanowires to generate excitation-emission energy maps. The observed two-dimensional maps reveal an OH field that has a non-linear dependence on excitation frequency. This study provides new insight into earlier reports of so-called avoidance and tracking, showing two distinct NSP responses directly by the addition of a emission energy axis. The data show that the polarization processes depend on which electron spin state is optically driven, with surprising differences in the polarization fluctuations for each case: in one case, a stabilized field characterized by a single-peaked distribution shifts monotonically with the laser excitation frequency resulting in a nearly constant optical interaction strength across a wide detuning range, while in the other case the previously reported avoidance behavior is actually the result of a nonlinear dependence on the laser excitation frequency near zero detuning leading to switching between two distinct mesoscopic nuclear spin states. The magnitude of the field, which is as large as 400 mT, is measured with sub-100 nuclear spin sensitivity. Stable/unstable points of the OH field distribution are observed, resulting from the non-linear feedback loop in the electron-trion-nuclear system. Nuclear spin polarization state switching occurs between fields differing by 160 mT at least as fast as 25 ms. Control experiments indicate that the strain-induced quadrupolar interaction may explain the measured OH fields.
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