Theory of the Absorption Spectrum
In comparison with the spectrum of the quantized electromagnetic (EM)1,2 field very little work has been done on the theory of the absorption spectrum. Generally speaking this refers to the absorption of energy from a weak monochromatic incident (polarization ê) field by a quantum system with which it interacts, considered as a function of the incident probe field frequency w. The quantum system could for example consist of an atom, or an atom driven by a strong laser field, and is taken to include the various reservoirs (such as spontaneous emission modes, ensembles of collider atoms etc.) which are coupled to the primary absorber of the weak probe field. The system in which the absorption occurs could have a variety of time dependences specified, as we will see, in terms of the behaviour of the trace TrS([u ε − (t), μ ε + (t + τ)]ρS(0)) (where μ ε + ,μ ε − are Heisenberg operators for the ê components of the parts of the system dipole operator producing upward, downward transitions, and ρS(0) is the system density operator at t = 0, at which time the Heisenberg operators equal the corresponding Schrodinger operators). This could be of a transient character (trace → 0 at t, τ → ∞) thereby allowing the absorption to occur only over a finite time interval. Such a case would occur for a two level atom driven by near resonant laser light with the upper state subject to photoionization, for example by a second laser beam. The absorption of a weak probe, tuned to near resonance with the ground to upper state transition, would be cut off by the loss of the atom to ionization.
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