No, the United States should not officially apologize for dropping the atomic bombs on Japan. There is good reason for countries to apologize for atrocities, but the atomic bombing of Japan was not an atrocity. It was a regular act of war.
First, we have to realize that the atomic bombs were not, in many ways, worse than conventional weapons. It is true that they were terrible things, but it is also true that firebombing Tokyo was a terrible thing. In fact, essentially everything that happens in war is terrible. It is not as if the atomic bombs were qualitatively different from other weapons and other acts of war. Yes, people did die of radiation poisoning later. But people also died of the effects of hunger brought on by the US policy of sinking as many Japanese merchant ships as possible.
All sides in the war did things that caused indescribable suffering. That is what war is all about. There is no need for the US to apologize to Japan for the atomic bombs any more than there is a need for Japan to apologize for the attack on Pearl Harbor or the use of kamikazes against American warships.