You are PHUKKED!!!
edit: how does AK call a 3bet, knowing that either he is screwed direly by rockets/cowboys or at best he's up against rival AK or queens (if we're wishful). What, someone ejaculates preflop with AQ??? NO way man. You say villain is solid, he's solid enough to know that 3 bet ~ AK, QQ+ in all likelihood.
Then, when AK hits top pair (good v. QQ only) he merely CALLS. That's weak as hell. Nah.
When someone reveals they have a nicee (by 3 betting) the only hand a player-with-a-brain calls with is something that can outdraw due to implied odds. Ex: opponent "i have KK/AA maybe QQ!", hero calls with 78s, 55, etc. The LAST hand you want when villain screams monster is Ax. You lay infinite reverse implied odds (AK v. AA/KK, if a ace / king flops oopsie, or funnier yet, flop of AKx).
If this guy doesn't beat a pair on the turn, *I'll* pay you the pot.