  Eight Accreting Millisecond X-ray Pulsars (AMXPs) are known to date. Optical
and NIR observations carried out during quiescence give a unique opportunity to
constrain the nature of the donor star and to investigate the origin of the
observed quiescent luminosity at long wavelengths. Using data obtained with the
ESO-Very Large Telescope, we performed a deep optical and NIR photometric study
of the fields of XTE J1814-338 and of the ultracompact systems XTE J0929-314
and XTE J1807-294 during quiescence in order to look for the presence of a
variable counterpart. If suitable candidates were found, we also carried out
optical spectroscopy. We present here the first multi-band (VR) detection of
the optical counterpart of XTE J1814-338 in quiescence together with its
optical spectrum. The optical light curve shows variability in both bands
consistent with a sinusoidal modulation at the known 4.3 hr orbital period and
presents a puzzling decrease of the V-band flux around superior conjunction
that may be interpreted as a partial eclipse. The marginal detection of the
very faint counterpart of XTE J0929-314 and deep upper limits for the
optical/NIR counterpart of XTE J1807-294 are also reported. We also briefly
discuss the results reported in the literature for the optical/NIR counterpart
of XTE J1751-305. Our findings are consistent with AMXPs being systems
containing an old, weakly magnetized neutron star, reactivated as a millisecond
radio pulsar during quiescence which irradiates the low-mass companion star.
The absence of type I X-ray bursts and of hydrogen and helium lines in outburst
spectra of ultracompact (P_orb < 1 hr) AMXPs suggests that the companion stars
are likely evolved dwarf stars.
