In order to constrain the bolometric luminosities, dust properties and molecular gas content of giant Lyman alpha nebulae, the so-called Lyman alpha blobs, we have carried out a study of dust continuum and CO line emission in two well-studied representatives of this population at z ~ 3: a Lya blob discovered by its strong Spitzer MIPS 24um detection (LABd05; Dey et al. 2005) and the Steidel blob 1 (SSA22-LAB01; Steidel et al. 2000). We find that the spectral energy distribution of LABd05 is well described by an AGN-starburst composite template with L(FIR) = (4.0 +/- 0.5) x 10^12 Lsun, comparable to high-z sub-millimeter galaxies and ultraluminous infrared galaxies. New APEX/LABOCA 870um measurements rule out the reported SCUBA detection of the SSA22-LAB01 (S[850um] = 16.8 mJy) at the > 4sigma level. Consistent with this, ultra-deep Plateau de Bure Interferometer (PdBI) observations with ~2arcsec spatial resolution also fail to detect any 1.2mm continuum source down to ~0.45mJy per beam (3sigma). Combined with the existing (sub)mm observations in the literature, we conclude that the FIR luminosity of SSA22-LAB01 remains uncertain. No CO line is detected in either case down to integrated flux limits of (Snu dV) < 0.25--1.0 Jy km/s, indicating a modest molecular gas reservoir, M(H_2) < 1--3 x 10^10 Msun. The non-detections exclude, with high significance (12 sigma), the previous tentative detection of a CO(4-3) line in the SSA22-LAB01. The increased sensitivity afforded by ALMA will be critical in studying molecular gas and dust in these interesting systems.
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