Abstract
We study the dependence of the vacuum Rabi splitting (VRS) on frequency disorder, vibrations, near-field effects, and density in molecular polaritonics. In the mesoscopic limit, static frequency disorder alone can already introduce a loss mechanism from polaritonic states into a dark state reservoir, which we quantitatively describe, providing an analytical scaling of the VRS with the level of disorder. Disorder additionally can split a molecular ensemble into donor-type and acceptor-type molecules and the combination of vibronic coupling, dipole-dipole interactions, and vibrational relaxation induces an incoherent FRET (F\"orster resonance energy transfer) migration of excitations within the collective molecular state. This is equivalent to a dissipative disorder and has the effect of saturating and even reducing the VRS in the mesoscopic, high-density limit. Overall, this analysis allows to quantify the crucial role played by dark states in cavity quantum electrodynamics with mesoscopic, disordered ensembles.
Highlights
The strength of light-matter coherent exchanges is enhanced when confined light modes, such as provided by optical cavities, are utilized
For N ideal two-level quantum emitters, coupled to a cavity mode, a collective enhancement proportional to N 1/2 can be obtained [1]. This is evident in the scaling of the collective vacuum Rabi splitting (VRS) in cavity quantum electrodynamics [2,3,4]
Molecular polaritonics is characterized by emitters with large inhomogenous broadening, coupled to local vibrational baths and with strong near-field interactions, in which case analytical approaches are typically limited to only a few molecules and often with only one vibrational mode [20,21,22,23]
Summary
The strength of light-matter coherent exchanges is enhanced when confined light modes, such as provided by optical cavities, are utilized. We apply our formalism to molecular polaritonics where the interplay between static disorder, near-field couplings, and vibrational relaxation leads to a FRET process characterized by incoherent transfer of excitations from energetically higher donor-type to lower frequency, acceptor-type molecules (see Fig. 1) We map this problem into an incoherent dynamics in Lindblad form describing migration of excitation at rates analytically computable and derive the scaling law for the VRS with density applying the open system dynamics previously derived for pure two-level systems. The vibronic coupling is obtained as a harmonic approximation of a Morse potential surface by expanding the electronic potential landscapes around their minima: the difference between the minima in the ground and excited state leads to the Huang-Rhys factors λ2k Such a model is widely employed [20,21,40,41] especially for molecules in condensed matter environments, as fast vibrational relaxation insures that states with more than one vibrational excitation are never reached. All channels of dissipation are modeled as standard Lindblad superoperators with collapse operators a, σ j, b jk and loss rates κ, γ , k
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