Theory of molecular emission power spectra. I. Macroscopic quantum electrodynamics formalism

Abstract

We study the emission power spectrum of a molecular emitter with multiple vibrational modes in the framework of macroscopic quantum electrodynamics. The theory we present is general for a molecular spontaneous emission spectrum in the presence of arbitrary inhomogeneous, dispersive, and absorbing media. Moreover, the theory shows that the molecular emission power spectra can be decomposed into the electromagnetic environment factor and lineshape function. In order to demonstrate the validity of the theory, we investigate the lineshape function in two limits. In the incoherent limit (single molecules in a vacuum), the lineshape function exactly corresponds to the Franck–Condon principle. In the coherent limit (single molecules strongly coupled with single polaritons or photons) together with the condition of high vibrational frequency, the lineshape function exhibits a Rabi splitting, the spacing of which is exactly the same as the magnitude of exciton–photon coupling estimated by our previous theory [S. Wang et al., J. Chem. Phys. 151, 014105 (2019)]. Finally, we explore the influence of exciton–photon and electron–phonon interactions on the lineshape function of a single molecule in a cavity. The theory shows that the vibronic structure of the lineshape function does not always disappear as the exciton–photon coupling increases, and it is related to the loss of a dielectric environment.

Simple but accurate estimation of light-matter coupling strength and optical loss for a molecular emitter coupled with photonic modes

“…According to our previous works 35,36 , we have proven that the Schrödinger equation with the Hamiltonian in Eq. ( 1) and |ψ(t) in Eq.…”

“…The Hamiltonian of a two-electronic-state molecule with multi-vibrational modes coupled to a vacuum field in a di-electric environment can be expressed as 35,36 Ĥ ≡ |g…”

“…To study quantum dynamics of molecular fluorescence (spontaneous emission), we use a wavefunction ansatz based on the Wigner-Weisskopf theory as follows 35,36 ,…”

“…where K pol (t,t ′ ) is the memory kernel of polariton which has been defined in our previous studies [34][35][36] ,…”

“…Light-matter interaction plays a crucial role in various fields such as surface-enhanced Raman spectroscopy [1][2][3][4][5][6][7][8][9] , biosensing [10][11][12][13][14][15] , photosynthesis [16][17][18][19][20] , resonance energy transfer [21][22][23][24][25][26][27] , and molecular fluorescence [28][29][30][31][32][33][34][35][36] . Recently, due to advances in nanotechnology, the achievement of strong light-matter interaction [37][38][39][40][41] has motivated successive studies on the chemical properties of light-matter hybrid states, leading to the emergence of polariton chemistry [42][43][44][45][46] .…”