Frequency difference, nonidentical atoms

The parameters A and Ac allow us to gain physical insight into how the dipole-dipole interaction O12 and the frequency difference A can modify the dynamics of the two-atom system. The parameter A appears as a shift of the energies of the superposition systems, while Ac determines the magnitude of the coherent interaction between the superpositions. For Yl 2 / 0 and identical atoms the shift A / 0, but can vanish for nonidentical atoms. This occurs for... 

Thus, the condition V 2 = /1 1I2 for suppression of spontaneous emission from the antisymmetric state is valid for identical as well as nonidentical atoms, whereas the coherent interaction between the superpositions appears only for nonidentical atoms with different transition frequencies and/or spontaneous damping rates. 

We illustrate this effect in Fig. 4, where we plot the steady-state population of the state —) as a function of A/, for two different types of nonidentical atoms. In the first case the atoms have the same damping rates (Ti = T2) but different transition frequencies (A / 0), while in the second case the atoms have the same frequencies (A = 0) but different damping rates (T / T2). It is... 

By employing two nonidentical atoms of significantly different transition frequencies (A > T), it is possible to achieve the pure TPE state with the interatomic separation comparable to the resonant wavelength, and the antisymmetric state fully participating in the interaction. 

The collective states (35) are eigenstates of the system of two identical atoms. If the atoms are not identical, the situation becomes more complicated and we will discuss here some consequences of the fact that the atoms could have different transition frequencies and/or different spontaneous emission rates. When the atoms are nonidentical with different transition frequencies, the states (35) are no longer the eigenstates of the Hamiltonian (32). The diagonalization of the matrix (34) with A / 0 leads to the following eigenstates [43]... 

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