Coherence and decoherence in the interaction of light with atoms

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Abstract
Amplification without population inversion in a resonant V-type atomic medium is analyzed using the theory of quantum trajectories. A global view of the dynamics underlying the amplification is provided by a quantum stochastic process governing an interplay between coherence and decoherence. The quantum trajectories decompose into distinct “gain cycles” and “loss cycles” which determine, respectively, the emission and absorption spectra that might be calculated from perturbation theory. Two methods for calculating net gain are developed, motivated by complementary views of the exchange of energy between an atom and a probe field. One time averages the energy radiated continuously by the induced dipole, while the other determines probabilities for discontinuous energy exchange through the emission and absorption of individual quanta. In the latter case, the emission and absorption probabilities are evaluated as sums over probabilities for classical records that define the unobservable exchange of a quantum with the probe field in terms of observable scattering events. Quantum trajectories for a V-type medium driven by a coherent field are compared with those for a medium driven incoherently. Two relationships which connect amplification to population inversion in the latter case are shown to be lacking in the former; hence the possibility for amplification without population inversion arises from the following: (1) a decoupling of the rate of gain-cycle (loss-cycle) initiation from the time-averaged population in the initial state for gain (loss), and (2) loss of the symmetry that the final state for emission be the initial state for absorption and vice versa. The specific influences of these general observations vary from model to model. The details are worked out for the resonant V-type medium, where the quantum trajectory analysis sheds light on the meaning of “without population inversion” and “cancellation of absorption by quantum interference.”