Atomic systems nonidentical atoms

We consider a system of two nonidentical and nonoverlapping atoms at positions ri and rj, coupled to the quantized three-dimensional electromagnetic held. The initial state of the held is the product of a single-mode coherent state of a driving laser held, and the vacuum state of the rest of the modes. Each atom is assumed to have only two levels the ground level g,) and the excited level e,)(i = 1,2), separated by an energy hot), =Ee. — Egi, and connected by an... 

Evidently, in the presence of the dipole-dipole interaction the matrix (34) is not diagonal, which indicates that the product states (33) are not the eigenstates of the two-atom system. We will diagonalize the matrix (34) for the case of identical (A = 0) as well as nonidentical (A / 0) atoms to find eigenstates of the system and their energies. 

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]... 

The choice of the collective states (40) as a basis leads to a complicated master equation whose physical properties are tractable only for very specific values of the parameters involved. A different choice of basis collective states is proposed here, which allows us to obtain a simple master equation of the system of two nonidentical atoms. Moreover, we will show that it is possible to create a maximally entangled state in the system of two nonidentical atoms that can be decoupled from the external environment and, at the same time, the state exhibits a strong coherent coupling with the remaining states. 

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... 

Guo and Yang [53] have analyzed spontaneous decay from two atoms initially prepared in an entangled state. They have shown that the time evolution of the population inversion, which is proportional to the intensity (87), depends on the degree of entanglement of the initial state of the system. Ficek et al. [10] have shown that in the case of two nonidentical atoms, the time evolution of the intensity 7(R, t) can exhibit quantum beats that result from the presence of correlations between the symmetric and antisymmetric states. In fact, quantum beats are present only if initially the system is in a nonmaximally entangled state, and no quantum beats are predicted for maximally entangled as well as unentangled states. 

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