We conduct a deep narrow-band imaging survey of 13 Ly \alpha blobs ( LABs ) located in the SSA22 proto-cluster at z \sim 3.1 in the C iv and He ii emission lines in an effort to constrain the physical process powering the Ly \alpha emission in LABs . Our observations probe down to unprecedented surface brightness limits of 2.1 – 3.4 \times 10 ^ { -18 } erg s ^ { -1 } cm ^ { -2 } arcsec ^ { -2 } per 1 arcsec ^ { 2 } aperture ( 5 \sigma ) for the He ii \lambda 1640 and C iv \lambda 1549 lines , respectively . We do not detect extended He ii and C iv emission in any of the LABs , placing strong upper limits on the He ii/Ly \alpha and C iv/Ly \alpha line ratios , of 0.11 and 0.16 , for the brightest two LABs in the field . We conduct detailed photoionization modeling of the expected line ratios and find that , although our data constitute the deepest ever observations of these lines , they are still not deep enough to rule out a scenario where the Ly \alpha emission is powered by the ionizing luminosity of an obscured AGN . Our models can accommodate He ii/Ly \alpha and C iv/Ly \alpha ratios as low as \simeq 0.05 and \simeq 0.07 respectively , implying that one needs to reach surface brightness as low as 1 – 1.5 \times 10 ^ { -18 } erg s ^ { -1 } cm ^ { -2 } arcsec ^ { -2 } ( at 5 \sigma ) in order to rule out a photoionization scenario . These depths will be achievable with the new generation of image-slicing integral field units such as VLT/MUSE or Keck/KCWI . We also model the expected He ii/Ly \alpha and C iv/Ly \alpha in a different scenario , where Ly \alpha emission is powered by shocks generated in a large-scale superwind , but find that our observational constraints can only be met for shock velocities v _ { s } \gtrsim 250 km s ^ { -1 } , which appear to be in conflict with recent observations of quiescent kinematics in LABs .