IRAM 30m-EMIR Redshift Search of z = 3-4 Lensed Dusty Starbursts selected from the HerBS sample

Using the EMIR instrument on the IRAM 30m telescope, we conducted a spectroscopic redshift search of seven z$_{rm phot}$ $sim$ 4 sub-millimetre bright galaxies selected from the Herschel Bright Sources (HerBS) sample with fluxes at 500 $mu$m greater than 80 mJy. For four sources, we obtained spectroscopic redshifts between 3.4 < z < 4.1 through the detection of multiple CO-spectral lines with J $leq$ 3. Later, we detected low-J transitions for two of these sources with the GBT including the CO(1-0) transition. For the remaining three sources, more data are needed to determine the spectroscopic redshift unambiguously. The measured CO luminosities and line widths suggest that all these sources are gravitationally lensed. These observations demonstrate that the 2 mm window is indispensable to confirm robust spectroscopic redshifts for z < 4 sources. Finally, we present an efficient graphical method to correctly identify spectroscopic redshifts.