  The subtle and fundamental issue of indistinguishability and interference
between independent pathways to the same target state is examined in the
context of coherent control of atomic and molecular processes, with emphasis
placed on possible "which-way" information due to quantum entanglement
established in the quantum dynamics. Because quantum interference between
independent pathways to the same target state occurs only when the independent
pathways are indistinguishable, it is first shown that creating useful
coherence (as defined in the paper) between nondegenerate states of a molecule
for subsequent quantum interference manipulation cannot be achieved by
collisions between atoms or molecules that are prepared in momentum and energy
eigenstates. Coherence can, however, be transferred from light fields to atoms
or molecules. Using a particular coherent control scenario, it is shown that
this coherence transfer and the subsequent coherent phase control can be
readily realized by the most classical states of light, i.e., coherent states
of light. It is further demonstrated that quantum states of light may suppress
the extent of phase-sensitive coherent control by leaking out some which-way
information while "incoherent interference control" scenarios proposed in the
literature have automatically ensured the indistinguishability of multiple
excitation pathways. The possibility of quantum coherence in photodissociation
product states is also understood in terms of the disentanglement between
photodissociation fragments. Results offer deeper insights into quantum
coherence generation in atomic and molecular processes.
