Which of the two sentences sound natural?
1. I have already submitted it on January 1, 2011.
2. I already submitted it on January 1, 2011.

I learned that we cannot use a present perfect tense with specific time expressions.
Also, I heard that it is unnatural to say "already" in a past tense.

If you want to emphasize "already" and "when it happens", what can you say?

Question

Which of the two sentences sound natural?
1. I have already submitted it on January 1, 2011.
2. I already submitted it on January 1, 2011.

I learned that we cannot use a present perfect tense with specific time expressions.
Also, I heard that it is unnatural to say "already" in a past tense.

If you want to emphasize "already" and "when it happens", what can you say?

Answer

I think that the best way is to say "I already submitted it, on January 1, 2011".  By using the comma, the specific date is extra information.
But, having said that, 2 is OK, as it is only trivially different, and even 1 is not noticeably unnatural.