Density matrix equation, coherent population dynamics

Figure 6. Coherent population dynamics calculated using the density matrix equation (3) for different delays (a-c) of the laser pulses. Upper part Time evolution of the Rabi frequencies of both laser pulses. Lower part Calculated time evolution of the level populations for three different delays.

A simple, non-selective pulse starts the experiment. This rotates the equilibrium z magnetization onto the v axis. Note that neither the equilibrium state nor the effect of the pulse depend on the dynamics or the details of the spin Hamiltonian (chemical shifts and coupling constants). The equilibrium density matrix is proportional to F. After the pulse the density matrix is therefore given by and it will evolve as in equation (B2.4.27). If (B2.4.28) is substituted into (B2.4.30), the NMR signal as a fimction of time t, is given by (B2.4.32). In this equation there is a distinction between the sum of the operators weighted by the equilibrium populations, F, from the unweighted sum, 7. The detector sees each spin (but not each coherence ) equally well. 

The purpose of this section is to show how to employ the density matrix method to study the population dynamics of a system. From the model shown in Fig. 4.2, we can see that due to the fact that there is only one system state, there is no system coherence (or phase). However, quantum beat may be observed under certain conditions. It should be noticed that the master equations of this model can be solved exactly and analytically. Likewise, its Schrodinger equation can also be solved exactly and analytically. 

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