Atomic systems steady-state populations

It is evident that the antisymmetric state is populated by the coherent coupling to the symmetric state. Since the decay rate of the antisymmetric state, T(1 — p), is very small for p 1, the population stays in this state for a long time. If A = 0 the state is decoupled from the symmetric state and is zero if its initial value is zero. In the latter case the system reduces to a two-level atom. In the former case the transfer of the population to a slowly decaying state leaves the symmetric state almost unpopulated even if the driving field is strong. This is shown in Fig. 17, where we plot the steady-state populations pss as a... 

In order to calculate the stationary state of the two-atom system, we have to know the steady-state populations pu of the collective atomic states and the coherencies Py(i 7 j)- First, we consider a system of two identical atoms (A = 0, Tj = r2) separated by an arbitrary distance rn and interacting with a squeezed vacuum field. Moreover, we assume that the carrier frequency (as of the squeezed vacuum field is resonant to the atomic transition frequencies (0)s = Mo). 

After transforming to the collective state basis, the master equation (31) leads to a closed system of 15 equations of motion for the density matrix elements [46]. However, for a specifically chosen geometry for the driving field, namely, that the field is propagated perpendicularly to the atomic axis (k rn = 0), the system of equations decouples into 9 equations for symmetric and 6 equations for antisymmetric combinations of the density matrix elements [45-50]. In this case, we can solve the system analytically, and find that the steady-state values of the populations are [45,46]... 

Fig. 4.7 Coherent population-trapping effect with optically oriented atoms (a) coherent population trapping between two levels (1 and 2) and an excited state 3 in a laser field with two frequencies (wi and LJ2), laser fields (b) steady-state excited-state population pss for a A-system as a function of the Raman detrming Sr, with the typical central dip associated with the coherent population-trapping phenomenon. (Adapted from Arimondo 1996.)...

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