Context : The structure in density and temperature of protoplanetary disks surrounding low-mass stars is not yet well known .
The protoplanetary disks mid-planes are expected to be very cold and thus depleted in molecules in gas phase , especially CO .
Recent observations of molecules at very low apparent temperature ( \sim 6 K ) challenge this current picture of the protoplanetary disk structures .

Aims : We aim at constraining the physical conditions , and in particular the gas-phase CO abundance in the mid-plane of protoplanetary disks .

Methods : The light molecule H _ { 2 } D ^ { + } is a tracer of cold and CO-depleted environment .
It is therefore a good candidate to explore the disks mid-planes .
We performed a deep search for H _ { 2 } D ^ { + } in the two well-known disks surrounding TW Hya and DM Tau using the APEX and JCMT telescopes .
The analysis of the observations are done with DISKFIT , a radiative transfer code dedicated to disks .
In addition , we used a chemical model describing deuterium chemistry to infer the implications of our observations on the level of CO depletion and on the ionization rate in the disks mid-plane .

Results : The ortho-H _ { 2 } D ^ { + } ( 1 _ { 1 , 0 } -1 _ { 1 , 1 } ) line at 372 GHz was not detected .
Although our limit is three times better than previous observations , comparison with the chemical modeling indicates that it remains insufficient to put valuable constraints on the CO abundance in the disk mid-plane .

Conclusions : Even with ALMA , the detection of H _ { 2 } D ^ { + } may not be straightforward , and H _ { 2 } D ^ { + } may not be a sufficiently sensitive tracer of the protoplanetary disks mid-plane .