Quantum interference master equation

The master equation will be derived by looking at the catalyst and its adsorbates in phase space. This is, of course, a classical mechanics concept, and one might wonder if it is correct to look at the reactions on an atomic scale and use classical mechanics. The situation here is the same as for the derivation of the rate equations for gas phase reactions. The usual derivations there also use classical mechanics. [5-9] Although it is possible to give a completely quantum mechanical derivation formalism, [10-13] the mathematical complexity hides much of the important parts of the chemistry. Besides, it is possible to replace the classical expressions that we will get by semi-quantum mechanical ones, in exactly the same way as for gas phase reactions. However, these expressions will not account for quantum efliects as tunneling and interference. 

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. 

In Fig. 2, we present the steady-state population inversion between the upper state 1) and the ground state 2), computed from the master equation (73), for r = 0 and different values of the phase difference 5<(> and the interference parameter p. It is seen that in the presence of quantum interference the population can be inverted on the 1) —> 2) transition and the inversion can be controlled by the phase difference between the driving laser fields [27],... 

The master equation (165) provides the basis for our analytical and numerical discussions of quantum interference effects in the molecular system. 

---