  Coupled nanolasers are of growing interest for on-chip optical computation
and data transmission, which requires an understanding of how lasers interact
to form complex systems. The non-Hermitian interaction between two coupled
resonators, when excited selectively, can lead to parity-time symmetry, the
formation of exceptional points, and subsequently spectral control and
increased sensitivity. These investigations have been limited to pump energies
close to the lasing threshold, and large or narrow-line lasers. Here, by
programmable optical excitation we study two coupled nanolasers significantly
above threshold, where mode instability plays an important role. We map the
mode evolution around two exceptional points, and observe lasing gaps due to
reversed pump dependence which compare well with nonlinear theory. Finally, the
coupling can be exploited to control the lasing threshold and wavelength, and
for frequency switching around the lasing gap. Controlled and integrated
nanolasers constitutes a promising platform for future highly sensitive and
programmable on-chip laser sources.
