  We present the results of a CO line survey of 30 galaxies at moderate
redshift (z \sim 0.2-0.6), with the IRAM 30m telescope, with the goal to follow
galaxy evolution and in particular the star formation efficiency (SFE) as
defined by the ratio between far-infrared luminosity and molecular gas mass
(LFIR/M(H2)). The sources are selected to be ultra-luminous infrared galaxies
(ULIRGs), with LFIR larger than 2.8 10^{12} Lsol, experiencing starbursts;
adopting a low ULIRG CO-to-H2 conversion factor, their gas consumption
time-scale is lower than 10^8 yr. To date only very few CO observations exist
in this redshift range that spans nearly 25% of the universe's age.
Considerable evolution of the star formation rate is already observed during
this period. 18 galaxies out of our sample of 30 are detected (of which 16 are
new detections), corresponding to a detection rate of 60%. The average CO
luminosity for the 18 galaxies detected is L'CO = 2 10^{10} K km/s pc^2,
corresponding to an average H2 mass of 1.6 10^{10} Msol. The FIR luminosity
correlates well with the CO luminosity, in agreement with the correlation found
for low and high redshift ULIRGs. Although the conversion factor between CO
luminosity and H2 mass is uncertain, we find that the maximum amount of gas
available for a single galaxy is quickly increasing as a function of redshift.
Using the same conversion factor, the SFEs for z\sim 0.2-0.6 ULIRGs are found
to be significantly higher, by a factor 3, than for local ULIRGs, and are
comparable to high redshift ones. We compare this evolution to the expected
cosmic H2 abundance and the cosmic star formation history.
