Why do you assume that athiesm and a belief in the possibility of life after death are not compatible?
Being an athiest myself, I’ve given a lot of thought to the subject, and I have to conclude that I just don’t know. I don’t believe there’s a God, but I believe there may be an infinite or near-infinite universe. Certainly the astronomical evidence we have suggests that the universe is either infinite or vastly bigger than the tiny part of it we can currently see.
If that’s the case, then there’s every possibility that my brain will show up again somewhere, which also contains the circuitry of the memories of this brain, just through sheer luck. After all, in an infinite universe, the improbable-yet-possible becomes certain. Would that make me ‘wake up’? Hell if I know. For all I know, every time I go to sleep I ‘die’, and when I wake up I just have the illusion of a continuous life because yesterday’s memories are still there when my new self wakes up.
What if the future holds a universe in which computing power continues to grow, until we have computing machines that are so much more powerful than a human brain that they can just randomly assemble the circuitry of entire brains, and create random memories? If this is iterated enough times, and the universe is infinite, then at some point my brain will be created again, and I might wake up.
Hell, the math shows that if the universe is infinite, there are already infinite earths out there, identical in every way to this one. Even if it’s not infinite, the probably of an identical ‘me’ being born is still greater than zero.
These are questions of physics and metaphysics - not questions of religion. As a skeptic and an athiest, I have to say that I have no evidence that I’ll ever perceive a thing again after this brain dies. But I can still contend with the possibility that I might.
To directly answer the OP, I guess my idea of ‘heaven’ would be a future in which some being or computer or random process recreates my brain, memories and all, and I ‘wake up’ again. Only this time in a future where there is technology to allow me to choose my own limits of consciousness and intellect and how long and on what terms I wish to continue living.
On the other hand, if this is what the future holds, then I’ll also have my brain created with bad memories, false memories, horrific pain impulses, or I’ll be a fleeting consciousness in a sea of false memories and strange mutations to who I am, from the barely changed to the unrecognizable. So it could also be my definition of hell.