We present a study of the quiescent optical counterpart of the Accreting Millisecond X-ray Pulsar XTE J1814-338, carrying out multiband (BVR) orbital phase-resolved photometry using the ESO VLT/FORS2. The optical light curves are consistent with a sinusoidal variability modulated with the orbital period, showing evidence for a strongly irradiated companion star, in agreement with previous findings. The observed colours cannot be accounted for by the companion star alone, suggesting the presence of an accretion disc during quiescence. The system is fainter in all analysed bands compared to previous observations. The R band light curve displays a possible phase offset with respect to the B and V band. Through a combined fit of the multi-band light curves we derive constraints on the companion star and disc fluxes, on the system distance and on the companion star mass. The irradiation luminosity required to account for the observed day-side temperature of the companion star is consistent with the spin-down luminosity of a millisecond radio pulsar. The flux decrease and spectral evolution of the quiescent optical emission observed comparing our data with previous observations, collected over 5 years, cannot be well explained with the contribution of an irradiated companion star and an accretion disc alone. The progressive flux decrease as the system gets bluer could be due to a continuum component evolving towards a lower, bluer spectrum. While most of the continuum component is likely due to the disc, we do not expect it to become bluer in quiescence. Hence we hypothesize that an additional component, such as synchrotron emission from a jet was contributing significantly in the earlier data obtained during quiescence and then progressively fading or moving its break frequency toward longer wavelengths.
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