  We present the results of deep optical imaging of the radio/$\gamma$-ray
pulsar PSR J2043+2740, obtained with the Large Binocular Telescope (LBT). With
a characteristic age of 1.2 Myr, PSR J2043+2740 is one of the oldest (non
recycled) pulsars detected in $\gamma$-rays, although with still a quite high
rotational energy reservoir ($\dot{E}_{\rm rot} = 5.6 \times 10^{34}$ erg
s$^{-1}$). The presumably close distance (a few hundred pc), suggested by the
hydrogen column density ($N_{\rm H} \lesssim 3.6 \times 10^{20}$ cm$^{-2}$),
would make it a viable target for deep optical observations, never attempted
until now. We observed the pulsar with the Large Binocular Camera of the LBT.
The only object (V=25.44$\pm$0.05) detected within ~3" from the pulsar radio
coordinates is unrelated to it. PSR J2043+2740 is, thus, undetected down to
V~26.6 (3-$\sigma$), the deepest limit on its optical emission. We discuss the
implications of this result on the pulsar emission properties.
