Coherence, quantum mechanical definition

To understand any coherence other than SQC, we need a new and more general definition of coherence. Coherence arises from the quantum mechanical mixing or overlap of spin states ( superposition ). In the two spin system (I, S = ll, 13C) we have four spin states (aa, up, pa, and PP), which are all stable states of defined energy. Let s talk about a single - C pair (one molecule). It is possible for this pair to be in any one of the four energy states, but it is also possible for the pair to be in a mixture or overlap or superposition of two states. This is one of the fundamental tenets of quantum mechanics Sometimes you cannot be sure which energy state a particle is in. Let s say that this particular pair is in a mixture of states aa and pp ... 

This is the operative technical term. It is equivalent to our earlier condition that there is a definite initial state and not an ensemble. The optically prepared state is then a pure state in the quantum mechanical sense, namely, it can be expressed as a superposition of states, each with its own phase, hence coherent. ... 

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