We present the search for the [CII] emission line in three $z>6.5$ Lyman-alpha emitters (LAEs) and one J-Dropout galaxy using the Combined Array for Research in Millimeter-wave Astronomy (CARMA) and the Plateau de Bure Interferometer (PdBI). We observed three bright $z\sim6.5-7$ LAEs discovered in the SUBARU deep field (SDF) and the Multiple Imaged lensed $z\sim 11$ galaxy candidate found behind the galaxy cluster MACSJ0647.7+7015. For the LAEs IOK-1 ($z=6.965$), SDF J132415.7+273058 ($z=6.541$) and SDF J132408.3+271543 ($z=6.554$) we find upper limits for the [CII] line luminosity of $<2.05$, $<4.52$ and $<10.56\times10^8\rm L_\odot$ respectively. We find upper limits to the FIR luminosity of the galaxies using a spectral energy distribution template of the local galaxy NGC 6946 and taking into account the effects of the Cosmic Microwave Background on the mm observations. For IOK-1, SDF J132415.7+273058 and SDF J132408.3+271543 we find upper limits for the FIR luminosity of $<2.33$, $3.79$ and $7.72\times10^11\rm L_\odot$ respectively. For the lensed galaxy MACS0647-JD, one of the highest redshift galaxy candidate to date with $z_\rm ph=10.7^+0.6_-0.4$ we put an upper limit in the [CII] emission of $<1.36\times10^8\times(\mu/15)^-1\rm L_\odot$ and an upper limit in the FIR luminosity of $<6.1\times10^10\times(\mu/15)^-1\rm L_\odot$ (where $\mu$ is the magnification factor). We explore the different conditions relevant for the search for [CII] emission in high redshift galaxies as well as the difficulties for future observations with ALMA and CCAT.
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