Multiplicity of Galactic Cepheids from long-baseline interferometry I. CHARA/MIRC detection of the companion of V1334 Cygni

Context. More than 60 % of Cepheids are in binary or multiple systems. Studying such systems could lead to a better understanding of the age and evolution of Cepheids. These are also useful tools to estimate the mass of Cepheids, and constrain theoretical models of their pulsation and evolution. Aims. We aim at determining the masses of Cepheids in binary systems, as well as their geometric distances and the flux contribution of the companions. The combination of interferometry with spectroscopy will offer a unique and independent estimate of the Cepheid masses. Methods. Using long-baseline interferometry at visible and infrared wavelengths, it is possible to spatially resolve binary systems containing a Cepheid down to milliarcsecond separations. Based on the resulting visual orbit and radial velocities, we can then derive the fundamental parameters of these systems, particularly the masses of the components and the geometric distance. We therefor