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The circumgalactic medium (CGM) is a crucial component of galaxy evolution,
but thus far its physical properties are highly unconstrained. As of yet, no
cosmological simulation has reached convergence when it comes to constraining
the cold and dense gas fraction of the CGM. Such components are also
challenging to observe, and require sub-millimeter instruments with a high
sensitivity to extended, diffuse emission, like the proposed Atacama Large
Aperture Sub-millimetre telescope (AtLAST). We present a state-of-the-art
theoretical effort at modeling the [CII], [CI](1-0), [CI](2-1), CO(3-2), and
[OIII] line emissions of galaxies. We use the high-resolution cosmological
zoom-in simulation Ponos, representing a star forming galaxy system at z = 6.5
($M_*=2\times10^9~M_{\odot}$), undergoing a major merger. We adopt different
modeling approaches based on the photoionisation code Cloudy. Our fiducial
model uses radiative transfer post-processing with RamsesRT and Krome to create
realistic FUV radiation fields, which we compare to sub-grid modeling
approaches adopted in the literature. We find significant differences in the
luminosity and in the contribution of different gas phases and galaxy
components between the different modeling approaches. [CII] is the least
model-dependant gas tracer, while [CI](1-0) and CO(3-2) are very
model-sensitive. In all models, we find a significant contribution to the
emission of [CII] (up to $\sim$10%) and [OIII] (up to $\sim$20%) from the CGM.
[CII] and [OIII] trace different regions of the CGM: [CII] arises from an
accreting filament and from tidal tails, while [OIII] traces a puffy halo
surrounding the main disc, probably linked to SN feedback. We discuss our
results in the context of current and future sub-mm observations with ALMA and
AtLAST.