Your assumption: Consciousness is determined by physical conditions e.g. the position, motion, charge etc. of atoms and the connections and activity state of the neurons in your brain.
Is this justified? I'm inclined to agree with you. Yet, this may be more an indication of ignorance rather than knowledge. I mean our current materialistic conceptualization of the universe prefers such a hypothesis. It sits pretty with current science.
I'm only concerned that there is a possibilty that this could be wrong. One thing that suggests such an error is the enormous difference between a stone and a bacteria. We can dissect apart a bacteria and study its parts in great detail. However, together, as a whole, it comes to life. We can look at another example from life. See the huge gap in cognitive function between humans and the rest of the animal kingdom. This gap is equivalent to, even more, than the gap between living and non-living. These observations lead me to believe that "the whole can be more than its parts".
As matter organizes at various levels and in different configurations, novel and strange phenomena occur. Could the human mind be one such thing? It develops from one such particular permutation of matter but lives in a different level of existence. Could it involve something a bit more than just placing atoms in position x, y, z?
This is pure speculation on my part and also it disagrees with scientific materialism and science has a proven track record. All I can say is if science is right on the money, it would suck as hell!
Let us assume that your assumption is true. What then do we make of the next part of your question?
It would appear that you would be exactly duplicated at another point. You would remember getting into the machine and then suddenly waking up in the new location, as if from a short nap. Now that I think of it, it would be very much like going to sleep/becoming unconscious at your home, then being taken to another location while you were asleep/unconscious and then waking up. In a sense, your thought experiment happens in real life.
In case, you don't get "atomized" and now there are two of you, it gets complicated (for me). Intuition tells me that now there would be two of you. However, the moment the two of you experience a different reality, your memories would be different from that point of time.
I guess we're now discussing what it means for you to be "you". Is there anything physically or mentally that defines you as "you" in a sort of unalterable way? Since memory is alterable, it hardly seems to qualify as a distinctive feature of identity. You stayed at home one day and you now have memories of a day at home. But, you could have easily gone to the park and developed a different memory. Does that mean, every time we have a choice between experiences, we're making choices about who we are? It doesn't seem right.
If you agree, then it implies there is a different set of properties that define your identity, that remains unchanged as you proceed through different experiences. What that is, I have no idea?