We analyze theoretically and experimentally how nonlinear differential-transmission spectroscopy of a lambda-system medium can provide quantitative understanding of the optical dipole moments and transition energies. We focus on the situation where two optical fields spatially overlap and co-propagate to a single detector. Nonlinear interactions give cross-modulation between a modulated and non-modulated laser field, yielding differential transmission signals. Our analysis shows how this approach can be used to enhance the visibility of relatively weak transitions, and how particular choices in the experimental design minimize systematic errors and the sensitivity to changes in laser field intensities. Experimentally, we demonstrate the relevance of our analysis with spectroscopy on the donor-bound exciton system of silicon donors in GaAs, where the transitions from the two bound-electron spin states to a bound-exciton state form a lambda system. Our approach is, however, of generic value for many spectroscopy experiments on solid-state systems in small cryogenic measurement volumes where in-situ frequency or polarization filtering of control and signal fields is often challenging.
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