  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. 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 therefore performed interferometric
observations of the first-overtone mode Cepheid V1334 Cyg with the CHARA/MIRC
combiner. We report the first detection of a Cepheid companion using
long-baseline interferometry. We detect the signature of a companion orbiting
V1334 Cyg at two epochs. We measure a flux ratio between the companion and the
Cepheid f = 3.10+/-0.08%, giving an apparent magnitude mH = 8.47+/-0.15mag. The
combination of interferometric and spectroscopic data have enabled the unique
determination of the orbital elements: P = 1938.6+/-1.2 days, Tp = 2 443
616.1+/-7.3, a = 8.54+/-0.51mas, i = 124.7+/-1.8{\deg}, e = 0.190+/-0.013,
{\omega} = 228.7+/-1.6{\deg}, and {\Omega} = 206.3+/-9.4{\deg}. We derive a
minimal distance d ~ 691 pc, a minimum mass for both stars of 3.6 Msol, with a
spectral type earlier than B5.5V for the companion star. Our measured flux
ratio suggests that radial velocity detection of the companion using
spectroscopy is within reach, and would provide an orbital parallax and
model-free masses.
