Theory for the stationary polariton response in the presence of vibrations

Abstract

We construct a model describing the response of a hybrid system where the electromagnetic field-in particular, surface plasmon polaritons-couples strongly with electronic excitations of atoms or molecules. Our approach is based on the input-output theory of quantum optics, and in particular it takes into account the thermal and quantum vibrations of the molecules. The latter is described within the P(E ) theory analogous to that used in the theory of dynamical Coulomb blockade. As a result, we are able to include the effect of the molecular Stokes shift on the strongly coupled response of the system. Our model then accounts for the asymmetric emission from upper and lower polariton modes. It also allows for an accurate description of the partial decoherence of the light emission from the strongly coupled system. Our results can be readily used to connect the response of the hybrid modes to the emission and fluorescence properties of the individual molecules, and thus are relevant in understanding any utilization of such systems, such as coherent light harvesting.

Molecule-photon interactions in phononic environments

“…It has been recently shown that the Purcell regime of cavity QED can result in a strong modification of the branching ratio of a single molecule and suppress undesired Stokes lines [12]. Recent theoretical works account for the vibronic coupling of molecules by solving a Holstein-Tavis-Cummings Hamiltonian which leads to the occurence of polaronpolariton states, i.e., light-matter states where the hybridized states between the bare electronic transition and the light field additionally get dressed by the vibrations of the molecules [15,[78][79][80][81][82][83][84]. Many models rely on numerical simulations and are based on following the evolution of state vectors under simplified assumptions assuming only vibronic interactions and finite temperature effects.…”

Polariton response in the presence of Brownian dissipation from molecular vibrations

“…However, the vibrations complicate finding the cavity reflection and transmission spectra notably as the equations of motion are nonlinear. The solution is obtained by moving into polaron frame, i.e., finding the dynamics of σ S = σe √ S(b † −b) , which allows for simplifying approximations that in the end decouple the vibrational dynamics from those of the cavity-exciton system 10,19 . The cavity transmission or emission spectrum is in this model…”

“…Furthermore, the same formalism extends to many vibrational modes: the total P (E) in Eq. ( 7) is then a convolution of all the single-mode P (E) functions 10 .…”

“…The correlator e ϕ(t) e −ϕ(0) can be evaluated for different models 10,19,20 so let us make a general argument: since the vibrations are harmonic, their fluctuations follow Gaussian statistics. Furthermore, we assume that these fluctuations are stationary, i.e., all correlators depend only on time differences and not on any specific time.…”

Plasmonic Purcell Effect in Organic Molecules

“…However, as plasmonic structures can achieve Purcell factors on the order of 10 6 [28], radiative decay rates can be decreased from their free-space values in the nanosecond range to femtoseconds, such that radiative decay does not proceed from vibrationally relaxed molecules, the FGR approximation breaks down, and non-equilibrium effects play an important role. More recently, cavity-QED approaches have been able to incorporate the interplay between the exciton and one (or a few) vibrational modes [33][34][35][36][37]. However, a realistic description of typical organic molecules could require considering hundreds of vibrational modes.…”