Multiple resonances involving magnetoexcitons in a ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_{0.30}{\mathrm{Ga}}_{0.70}\mathrm{As}$ quantum well

The excitonic states in an undoped ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_{0.30}{\mathrm{Ga}}_{0.70}\mathrm{As}$ single quantum well have been studied by magneto-photoluminescence excitation spectroscopy at $T=4.2\mathrm{}$ K. A series of regularly spaced steplike features is observed in the magnetic field dispersions of the transition energies of the excited heavy-hole excitons $\mathrm{ns}\mathrm{hh},\hspace{0.5em}n=2,3,4.\mathrm{}$ Correspondingly, the splitting between the two circular polarizations of the $2s\mathrm{hh}$ exciton shows pronounced oscillations as a function of magnetic field. We suggest that these features originate from the coupling of the transition between the ground state $1s\mathrm{hh}$ exciton and each of the excited states of the exciton with another excitation in the system. The energy difference between the features, which is about 7.5 meV, suggests that the excitation may be a transverse acoustic phonon with nonzero wave number near the zone boundary.