The atheist is still a Jew; his (non-)belief does not exempt him from the obligation not to violate Shabbat.
This answer elsewhere by DoubleAA discusses benefitting from melacha done by a Jew. It stands to reason that if you can't benefit from the work anyway, there's no benefit to you in asking him to be your "Shabbat goy", so let's look first at the case where there was no asking -- he just did it on his own. The answer there, citing OC 318:1 and Mishna Berurah and Biur Halacha there, says, in part:
If a biblical prohibition was violated purposefully (deoraita bemeizid) then no one can derive benefit from it for the rest of shabbat, and the violator himself cannot derive benefit forever.
If a rabbinic prohibition was violated purposefully (derabanan bemeizid) then no one including himself can derive benefit from it for the rest of shabbat and everyone is permitted to derive benefit after shabbat. (Some question this ruling and forbid him from deriving benefit from it forever.)
In other words, no.
This page from Halachipedia goes farther, saying that we must prevent other Jews from violating Shabbat if it is within our control, and also raising lifnei 'iver (placing a stumbling-block before the blind):
Just as observant Jews do not violate Shabbat, they equally have a responsibility to prevent other Jews from violating Shabbat when it is in their control. Asking a Jew to do work is a more serious transgression than asking a non-Jew, as it causes someone who is obligated to keep Shabbat to violate it. By asking a fellow Jew to violate Shabbat, the requester violates "Lifnei Iver lo Titen Michshal" - the issur forbidding a Jew to cause another Jew to violate a law he is obligated in. (39 Melachos (Rabbi Ribiat; vol 1, pg 91, footnote 354))
One should make sure neighbors that one may sometimes ask favors from on Shabbat are in fact not Jewish and not merely not religious Jews. (Gemara 150a and Ritva 150a "may shna...")
I haven't checked the cited sources but I find the reasoning to be sound.