Theoretical Development: Two-Pump Optical Scheme for Selective Electron-Nuclear Spin Interaction and Overhauser Field Strength

We present the theoretical development of a two-pump scheme to provide enhanced control over the strength of optically pumped nuclear spin polarization in GaAs via pump-probe spectroscopy. Building on a one-pump model of electron spin polarization, we introduce a second pump to manipulate the degree of nuclear spin polarization along an external magnetic field for arbitrary pump-pump temporal separations. While the one-pump model depends on the pulsed laser repetition rate, the two-pump scheme allows for mode-locking that is no longer entirely dependent on the repetition rate, enabling control over multiple mode-locked frequencies and finer control over electron-nuclear spin interaction strength. This flexibility provides fine adjustment of the Overhauser field (i.e., the nuclear magnetic field) and more precise tuning of the nuclear-induced frequency focusing effect and the electron spin Larmor precession frequency. Consequently, the two-pump model expands the range of experimental control and offers versatility beyond that of the one-pump model, providing a foundational approach for nuclear spin system manipulation.