We present a derivation of the star formation rate per comoving volume of quasar host galaxies , derived from stacking analyses of far-infrared to mm-wave photometry of quasars with redshifts 0 < z < 6 and absolute I -band magnitudes -22 > I _ { AB } > -32 We use the science demonstration observations of the first \sim 16 deg ^ { 2 } from the Herschel Astrophysical Terahertz Large Area Survey ( H-ATLAS ) in which there are 240 quasars from the Sloan Digital Sky Survey ( SDSS ) and a further 171 from the 2dF-SDSS LRG and QSO ( 2SLAQ ) survey .
We supplement this data with a compilation of data from IRAS , ISO , Spitzer , SCUBA and MAMBO .
H-ATLAS alone statistically detects the quasars in its survey area at > 5 \sigma at 250 , 350 and 500 \mu m. From the compilation as a whole we find striking evidence of downsizing in quasar host galaxy formation : low-luminosity quasars with absolute magnitudes in the range -22 > I _ { AB } > -24 have a comoving star formation rate ( derived from 100 \mu m rest-frame luminosities ) peaking between redshifts of 1 and 2 , while high-luminosity quasars with I _ { AB } < -26 have a maximum contribution to the star formation density at z \sim 3 .
The volume-averaged star formation rate of -22 > I _ { AB } > -24 quasars evolves as ( 1 + z ) ^ { 2.3 \pm 0.7 } at z < 2 , but the evolution at higher luminosities is much faster reaching ( 1 + z ) ^ { 10 \pm 1 } at -26 > I _ { AB } > -28 .
We tentatively interpret this as a combination of a declining major merger rate with time and gas consumption reducing fuel for both black hole accretion and star formation .