  Linear in the wave-vector terms of an electron Hamiltonian play an important
role in topological insulators and spintronic devices. Here we demonstrate how
an external electric field controls the magnitude of a linear-in-K term in the
exciton Hamiltonian in wide GaAs quantum wells. The dependence of this term on
the applied field in a high quality sample was studied by means of the
differential reflection spectroscopy. An excellent agreement between the
experimental data and the results of calculations using semi-classical
non-local dielectric response model confirms the validity of the method and
paves the way for the realisation of excitonic Datta-and-Das transistors. In
full analogy with the spin-orbit transistor proposed by Datta and Das [Appl.
Phys. Lett. {\bf 56}, 665 (1990)], the switch between positive and negative
interference of exciton polaritons propagating forward and backward in a GaAs
film is achieved by application of an electric field with non-zero component in
the plane of the quantum well layer.
