Dipole moments master equation

In this section, we present a derivation of the master equation for the density operator of two arbitrary dipole moments driven by an external field and... 

Equation (64) is the final form of the master equation that gives us an elegant description of the physics involved in the dynamics of two interacting systems. An important point is that the master equation is quite general and can be applied to an arbitrary system composed of two dipole moments. 

The presence of the additional damping terms F12 may suggest that quantum interference enhances spontaneous emission from two coupled systems. However, as we shall illustrate in the following sections, the presence of these terms in the master equation can, in fact, lead to a reduction or even suppression of spontaneous emission. According to Eq. (62), the reduction and suppression of spontaneous emission can be controlled by changing the mutual orientation of the dipole moments of the bare systems. 

The spectrum of the fluorescence field emitted on the 1) —> 2) and 13) —> 12) transitions is given by the Fourier transform of the average two-time correlation function of the dipole moments of the transitions that, according to the quantum regression theorem [33], satisfy the same equations of motion as the density matrix elements pj2( ) and P32W- Using the master equation (64) with the Hamiltonian (82), we obtain the following set of coupled equations of motion for the density matrix elements... 

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