Magneto-absorption spectra of hydrogen-like yellow exciton series in cuprous oxide: excitons in strong magnetic fields

We study the absorption spectra of the yellow excitons in Cu$_2$O in high magnetic fields using polarization-resolved optical absorption measurements with a high frequency resolution. We show that the symmetry of the yellow exciton results in unusual selection rules for the optical absorption of polarized light and that the mixing of ortho- and para- excitons in magnetic field is important. Our calculation of the energies of the yellow exciton series in an arbitrary magnetic field gives an excellent fit to experimental data and allows us to understand the complex structure of excitonic levels and their magnetic field dependence, which resolves the old-standing disagreement between the results of optical absorption and cyclotron resonance measurements.