  The Fermi Large Area Telescope (LAT) discovered the time signature of a
radio-silent pulsar coincident with RX J0007.0+7302, a plerion-like X-ray
source at the centre of the CTA 1 supernova remnant. The inferred timing
parameters of the gamma-ray pulsar PSR J0007+7303 (P=315.8 ms; dot{P}\sim3.6
10^{-13} s s^{-1}) point to a Vela-like neutron star, with an age comparable to
that of CTA 1. The PSR J0007+7303 low distance (\sim 1.4 kpc), interstellar
absorption (A_V\sim 1.6), and relatively high energy loss rate (dot{E} \sim4.5
10^{35} erg s^{-1}), make it a suitable candidate for an optical follow-up.
Here, we present deep optical observations of PSR J0007+7303. The pulsar is not
detected in the Gran Telescopio Canarias (GTC) images down to a limit of r'\sim
27.6 (3 sigma), the deepest ever obtained for this pulsar, while William
Herschel Telescope (WHT) images yield a limit of V \sim 26.9. Our r'-band limit
corresponds to an optical emission efficiency \eta_{opt}= L_{opt}/dot{E} < 9.4
10^{-8}. This limit is more constraining than those derived for other Vela-like
pulsars, but is still above the measured optical efficiency of the Vela pulsar.
We compared the optical upper limits with the extrapolation of the XMM-Newton
X-ray spectrum and found that the optical emission is compatible with the
extrapolation of the X-ray power-law component, at variance with what is
observed, e.g. in the Vela pulsar.
