Quantum theory of the optical pumping

In the optical sense the source is incoherent and the total density matrix of the ensemble of atoms can therefore be separated into density matrices and belonging to the ground and excited states, respectively. In Chapters 15 and 16 we have shown how p can be calculated in a number of different physical situations. In the present experiments the calculation of p may need to be modified slightly to take account of finite ground-state coherences, since can no longer be assumed to be diagonal. 

Following a discussion similar to that given in section 15.5 it can be shown that the Liouville equation for the ground-state density matrix is given by 

The commutator bracket [JfQ.Pg] describes the time-development of the system under the effects of the atomic Hamiltonian and of any static external magnetic field, while the last three terms give the evolution under the influence of depopulation pumping, repopulation pumping, and relaxation processes respectively. These processes are considered separately in the sections which follow. 

Detailed solutions of equation (17.32) result not only in expressions for the populations of the different ground- 

For the moment we assume that no coherence exists in the ground state and that the atoms are illuminated with light of broad spectral profile. Then the rate, at 

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