We present high-resolution near-infrared spectra taken during eight transits of 55 Cancri e, a nearby low-density super-Earth with a short orbital period (< 18 hours). While this exoplanets bulk density indicates a possible atmosphere, one has not been detected definitively. Our analysis relies on the Doppler cross-correlation technique, which takes advantage of the high spectral resolution and broad wavelength coverage of our data, to search for the thousands of absorption features from hydrogen-, carbon-, and nitrogen-rich molecular species in the planetary atmosphere. Although we are unable to detect an atmosphere around 55 Cancri e, we do place strong constraints on the levels of HCN, NH${}_3$, and C${}_2$H${}_2$ that may be present. In particular, at a mean molecular weight of 5 amu we can rule out the presence of HCN in the atmosphere down to a volume mixing ratio (VMR) of 0.02%, NH${}_3$ down to a VMR of 0.08%, and C${}_2$H${}_2$ down to a VMR of 1.0%. If the mean molecular weight is relaxed to 2 amu, we can rule out the presence of HCN, NH${}_3$, and C${}_2$H${}_2$ down to VMRs of 0.001%, 0.0025%, and 0.08% respectively. Our results reduce the parameter space of possible atmospheres consistent with the analysis of HST/WFC3 observations by Tsiaras et al. (2016), and indicate that if 55 Cancri e harbors an atmosphere, it must have a high mean molecular weight and/or clouds.
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