  (abridged) PSR J1048-5832 is a young Vela-like pulsar that was recently
detected in gamma-rays with Fermi, and also in X-rays with Chandra and
XMM-Newton. It powers a compact PWN visible in X-rays. We present deep optical
observations with the ESO Very Large Telescope to search for optical
counterparts of the pulsar and its nebula and to explore their multi-wavelength
emission properties. The data were obtained in V and R bands and compared with
archival data in other spectral domains. We do not detect the pulsar in the
optical and derive informative upper limits of R > 28.1 mag and V > 28.4 mag
for its brightness. Using a red-clump star method, we estimate an interstellar
extinction towards the pulsar of 2 mag, which is consistent with the absorbing
column density derived form X-rays. The respective distance agrees with the
dispersion measure distance. We reanalyse the Chandra X-ray data and compare
the dereddened upper limits with the unabsorbed X-ray spectrum of the pulsar.
We find that regarding its optical-X-ray spectral properties this gamma-ray
pulsar is not distinct from other pulsars detected in both ranges. However,
like the Vela pulsar, it is very inefficient in the optical and X-rays. Among a
dozen optical sources overlapping with the pulsar X-ray nebula we find one with
V = 26.9 and R = 26.3 mag, whose colour is slightly bluer then that of the
field stars and consistent with the peculiar colours typical for pulsar nebula
features. It positionally coincides with a relatively bright feature of the
pulsar X-ray nebula, resembling the Crab wisp and locating in 2 arcsec from the
pulsar. We suggest this source as a counterpart candidate to the feature. Based
on the substantial interstellar extinction towards the pulsar and its optical
inefficiency, further optical studies should be carried out at longer
wavelengths.
