  Local starbursts have a higher efficiency of converting gas into stars, as
compared to typical star-forming galaxies at a given stellar mass, possibly
indicative of different modes of star formation. With the peak epoch of galaxy
formation occurring at z > 1, it remains to be established whether such an
efficient mode of star formation is occurring at high-redshift. To address this
issue, we measure the molecular gas content of seven high-redshift (z ~ 1.6)
starburst galaxies with the Atacama Large (sub-)Millimeter Array and
IRAM/Plateau de Bure Interferometer. Our targets are selected from the sample
of Herschel far-infrared detected galaxies having star formation rates
(~300-800 Msolar/yr) elevated (>4x) above the star-forming `main sequence', and
included in the FMOS-COSMOS near-infrared spectroscopic survey of star-forming
galaxies at z ~ 1.6 with Subaru. We detect CO emission in all cases at high
levels of significance, indicative of high gas fractions (~30-50%). Even more
compelling, we firmly establish with a clean and systematic selection that
starbursts, identified as main-sequence outliers, at high redshift generally
have a lower ratio of CO to total infrared luminosity as compared to typical
main-sequence star-forming galaxies, although with a smaller offset than
expected based on past studies of local starbursts. We put forward a hypothesis
that there exists a continuous increase in star formation efficiency with
elevation from the main sequence with galaxy mergers as a possible physical
driver. Along with a heightened star formation efficiency, our high-redshift
sample is similar in other respects to local starbursts such as being metal
rich and having a higher ionization state of the interstellar medium.
