We report the detection of CN(N=3-2) emission towards the Cloverleaf quasar (z=2.56) based on observations with the IRAM Plateau de Bure Interferometer. This is the first clear detection of emission from this radical at high redshift. CN emission is a tracer of dense molecular hydrogen gas (n(H2) > 10^4 cm^{-3}) within star-forming molecular clouds, in particular in regions where the clouds are affected by UV radiation. The HCN/CN intensity ratio can be used as a diagnostic for the relative importance of photodissociation regions (PDRs) in a source, and as a sensitive probe of optical depth, the radiation field, and photochemical processes. We derive a lensing-corrected CN(N=3-2) line luminosity of L(CN(3-2) = (4.5 +/- 0.5) x 10^9 K km/s pc^2. The ratio between CN luminosity and far-infrared luminosity falls within the scatter of the same relationship found for low-z (ultra-) luminous infrared galaxies. Combining our new results with CO(J=3-2) and HCN(J=1-0) measurements from the literature and assuming thermal excitation for all transitions, we find a CO/CN luminosity ratio of 9.3 +/- 1.9 and a HCN/CN luminosity ratio of 0.95 +/- 0.15. However, we find that the CN(N=3-2) line is likely only subthermally excited, implying that those ratios may only provide upper limits for the intrinsic 1-0 line luminosity ratios. We conclude that, in combination with other molecular gas tracers like CO, HCN, and HCO+, CN is an important probe of the physical conditions and chemical composition of dense molecular environments at high redshift.
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