  Swift J1749.4-2807 is a transient accreting millisecond X-ray pulsars, the
first that displayed X-ray eclipses. Therefore it holds a great potential for
accurate mass measurements in a low mass X-ray binary system. The determination
of the companion star radial velocity would make it possible to fully resolve
the system and to accurately measure the mass of the neutron star based on
dynamical measurements. Unfortunately, no optical/NIR counterpart has been
identified to date for this system, either in outburst or in quiescence. We
performed a photometric study of the field of Swift J1749.4-2807 during
quiescence in order to search for the presence of a variable counterpart. The
source direction lies on the Galactic plane, making any search for its
optical/NIR counterpart challenging. To minimize the effects of field crowding
and interstellar extinction, we carried out our observations using the adaptive
optics near-infrared imager NACO mounted at the ESO Very Large Telescope. From
the analysis of Swift X-ray data obtained during outburst, we derived the most
precise (1.6" radius) position for this source. Due to the extreme stellar
crowding of the field, 41 sources are detected in our VLT images within the
X-ray error circle, with some of them possibly showing variability consistent
with the expectations. We carried out the first deep imaging campaign devoted
to the search of the quiescent NIR counterpart of Swift J1749.4-2807. Our
results allow to provide constraints on the nature of the companion star of
this system. Furthermore, they suggest that future phase-resolved NIR
observations (performed with large aperture telescopes and adaptive optics)
covering the full orbital period of the system are likely to identify the
quiescent counterpart of Swift J1749.4-2807, through the measure of its orbital
variability, opening the possibility of dynamical studies of this unique
source.
