  Context. The benchmark open cluster M67 is known to have solar metallicity
and similar age as the Sun. It thus provides us a great opportunity to study
the properties of solar twins, as well as the evolution of Sun-like stars.
Aims. Previous spectroscopic studies reported to detect possible subtle changes
in stellar surface abundances throughout the stellar evolutionary phase, namely
the effect of atomic diffusion, in M67. In this study we attempt to confirm and
quantify more precisely the effect of atomic diffusion, as well as to explore
the level of chemical (in)homogeneity in M67. Methods. We presented a strictly
line-by-line differential chemical abundance analysis of two groups of stars in
M67: three turn-off stars and three sub-giants. Stellar atmospheric parameters
and elemental abundances were obtained with very high precision using the
Keck/HIRES spectra. Results. The sub-giants in our sample show negligible
abundance variations ($\le$ 0.02 dex), which implies that M67 was born
chemically homogeneous. We note there is a significant abundance difference
($\sim$ 0.1 - 0.2 dex) between sub-giants and turn-off stars, which can be
interpreted as the signature of atomic diffusion. Qualitatively stellar models
with diffusion agree with the observed abundance results. Some turn-off stars
do not follow the general pattern, which suggests that in some cases diffusion
can be inhibited, or they might suffered some sort of mixing event related to
planets. Conclusions. Our results pose additional challenges for chemical
tagging when using turn-off stars. In particular, the effects of atomic
diffusion, which could be as large as 0.1 - 0.2 dex, must be taken into account
in order for chemical tagging to be successfully applied.
