Optical observation of the energy-momentum dispersion of spatially indirect excitons

The center-of-mass (CM) dispersion of spatially indirect excitons (IE’s) in biased ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_{0.35}{\mathrm{Ga}}_{0.65}\mathrm{As}$ double quantum wells is determined by photoluminescence (PL) spectroscopy in an in-plane magnetic field B. The field rigidly shifts the IE dispersion in k space by an amount proportional to both B and the electron-hole separation. The PL emission arises from IE’s with zero total momentum, corresponding to finite CM velocity, which allows the direct measurement of the IE CM dispersion. The observed PL energy increases quadratically in B, corresponding to the IE kinetic energy, whereas the PL intensity follows the thermal occupation of the optically active IE states and decreases as a Gaussian function of B.