Linear Response Theory of Natural Optical Activity

3 Linear Response Theory of Natural Optical Activity 

The general statement that connects quantum theory to experimental observations such as optical activity can be put as follows. We subject the material medium to some experimental procedure using a probe light beam, and observe a certain outcome after the probe has passed through the system, for example by analysing the scattered light. If we define the density matrix tot for the combined system of material medium + probe, and characterize the measurement by some operator, then the probability that the specified outcome of the measurement is observed, is given by, 

In the particular case of optical activity I can describe the experiment by choosing % to be the electric polarization operator P(x, t) for the material medium, while tot refers to the combined system of matter interacting with the polarized light beam. Note that [ tot P] = 0, where P is the space-inversion operator (see40 and Sect. 4). Then the mean value, 

Hie coupling between the medium and the light beam is described by the interaction Hamiltonian, 

The interaction between the matter and the light beam is weak and I compute the state TOt using perturbation theory based on the complete set of exact states / , with energies ha of the chiral medium in the absence of the light beam, noting that the information yielded by the experiment can then be related to the optically active medium alone. The density matrix, , for the medium in the absence of the light beam can be given a spectral representation in terms of this complete set of states, by virtue of the spectral theorem, 

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