Steep dispersion and coherent control of Faraday rotation in a potassium vapor cell

Electromagnetically induced transparency (EIT) was studied in a heated vapor cell of potassium without buffer gas or anti-relaxation coating. Transparency windows 60 times narrower than the natural line width and group indices exceeding 6000 were generated using a simple optical setup with a single free-running laser and an acousto-optic modulator. A longitudinal magnetic field was used to split the EIT feature into three components for either lin$\perp$lin or lin$\parallel$lin polarizations of probe and coupling beams. Measurements of polarization rotation revealed that only the lin$\parallel$lin configuration leads to circular birefringence, an effect which we attribute to quantum interference between the multiple $\Lambda$-type subsystems contributing to the signal. The Verdet constant of the EIT medium was measured to be $(5.8\pm 0.3)\times 10^4$ rad/T/m, and a novel measurement of group index for circular polarization based on birefringence was demonstrated. For larger fields, where the individual peaks were well resolved, resonant polarization rotations of $(210\pm10)$ mrad/MHz were observed.