  ::I suggest you read the article on quantum superposition. The basic idea: they prepared and measured the system in the same way many times. Some of the times they measured that the system was in its ground state, and some of the time it was in its first excited state. From the statistics of many measurements, they infer the original quantum state, which is a superposition of the ground and first excited state. Also, it may not be a great idea to base one's understanding of physics on Ted talks.   