This question is similar to "What causes the collective emission in Dicke Model?", but more specific. I wonder if the situation described in
[1] R. H. Dicke – Coherence in Spontaneous Radiation Processes. Physical Review 93(1), 99–110 (1954)
generally describes dipole-coupled emitters, as for example experimentally shown in
The theoretical model for 2 emitters is derived for example in
Dicke [1] describes gas in a transparent sub-wavelength vessel, where
all the molecules are interacting with a common radiation field and hence cannot be treated as independent.Moreover, the molecules are considered as two-level-systems with identical transition frequencies. The Hamiltonian of the system consists of the excited-state energy of all molecules (Eq. 4) plus a field interaction term for each molecule (Eq. 15). He then shows that some initial states have increased/decreased emission rates.
Akram et al. [3] describe a situation with exactly 2 emitters, but include an additional set of parameters, like different resonance frequencies $\omega_1$, $\omega_2$, arbitrary relative position and orientation and even different decay rates $\Gamma_1$, $\Gamma_2$. The Hamiltonian is the sum of the excited-state energies, the energy of all electromagnetic modes, an interaction between each emitter and the electromagnetic field (and a laser drive term) (Eq. 2). Using the Lindblad master equation (which wasn't developed in Dicke's time), they derive a general expression for the interaction energy $\delta_{12} \sim {r_{12}}^{-3}$ due to the coupling to common electromagnetic modes (Eq. 25) as function of the relative position $r_{12}$ of the emitters. This leads to a hybridization of the energy eigenstates into super- and subradiant states, with decay rate faster/slower by the cross-damping rate $\Gamma_{12} \sim \sqrt{\Gamma_1 \Gamma_2}$.
- My question is:
- Is the origin of super-/subradiance in both theories the same or am I missing subtle differences? In [3] they cite [1], but not in a context which makes clear that they describe the same phenomenon. What confused me in Dicke's paper [1] is in particular a remark on the first page that "dipole-dipole interaction is negligible".
