Control of the Stokes Shift with Strong Coupling

Abstract

A stronger coupling can be achieved if a molecule is placed into a small resonant Fabry-Perot cavity or to a vicinity of a nanostructure supporting surface plasmon (SP) resonance. The time evolution of the two coupled oscillators, e.g., a cavity and a molecule, can be described as a linear superposition of their normal hybrid modes. [4] The even (odd) oscillation mode has the higher (lower) frequency, ω ± = ω 0 ± Δ, and corresponds to the upper (lower) branch of the dispersion curve. (Here Δ is the coupling frequency and the frequencies of uncoupled oscillators ω 0 are assumed to be the same.) If Δ exceeds all relaxation rates in the system, the dispersion curve features the avoided crossing and the well-resolved energy gap known as the normal mode splitting or the Rabi splitting [4,5] (Figure 1a,b). This criterion does not require the coupling to be large, [3,4] e.g., ≈5 meV, [6] as long as all relaxation processes of importance are sufficiently slow. This is often the case of single quantum emitters coupled to cavities. [7,8] We also propose in Figure 1c,d a model to explain this splitting behavior, which shall be discussed in detail shortly.On the other hand, as the splitting energy 2Δ is getting comparable to ω 0 , one enters the so-called ultrastrong coupling regime. [9] This is the case of large ensembles of dye molecules coupled to plasmonic nanostructures and resonant cavities, which routinely leads to the normal mode splitting (proportional to the square root of the molecular number density / N V ) [4] of the order of 1 eV. [10] Such a large change in the eigenvalues of the hybrid modes paves the way to unprecedented control of electrical conductivity, [11] excitation transport, [12] surface potential, [13] and rates of chemical reactions. [9] Early research of the strong coupling was focused on quantum wells in resonant Bragg cavities. [5] In more recent years, this phenomenon has been studied at low and high (room) temperatures in multiple quantum and classical systems, including quantum dots, [7] single molecules, [8] and large molecular ensembles [14,15] interacting with localized and propagating SPs, [15,16] and cavities. [8,9,17] In spite of large-scale theoretical and experimental efforts, some fundamental aspects of the strong coupling remain to be unexplored. One of them is the debated applicability of the quantum mechanical model to large ensembles of molecules, which may be possible if the latter act as one "giant atom," [4] providing for coherent spontaneous emission, [18,19] and energy oscillations. [20] This fundamental question and the intriguing Strong coupling of excitons in macroscopic ensembles of quantum emitters and cavities (or surface plasmons) can lead to dramatic change of the optical properties and modification of the dispersion curves, characterized by the normal mode splitting of the order of 1 eV. Such gigantic alteration of the hybrid energy states enables scores of unparalleled physical phenomena and functionalities, ranging from enhancement of electrical conductivity to co...

Suppression of photo-oxidation of organic chromophores by strong coupling to plasmonic nanoantennas

“…In particular, it has been shown recently that chemical reactivity (19,(23)(24)(25) and charge and exciton transport (26)(27)(28) can be modified under strong coupling conditions. Strong coupling has been demonstrated to tune the work-function (29), as well as to control the Stokes shifts of hybridized molecules (30). Feist et al (24) have theoretically described an increased stability in the strong coupling regime for a photo-isomerization reaction.…”

Coupling of the First and Second Excited States of R6G Dye with the Fabry–Perot Cavity

“…It has been shown that when dye molecules are strongly coupled to a cavity, the emission originating from the low‐energy polariton branch is not observed when the system is pumped into the same branch. This effect was explained in terms of parity forbidden transitions within the same excited state parabola. The same arguments should be applicable to the transition between the low‐energy polariton branch of the hybridized S 2 state and the low‐energy polariton branch of the hybridized S 1 state.…”

“…The used amounts of R6G and PMMA resulted in the dye concentration (in solid state) equal to 2.69 × 10 20 cm −3 , equivalent to 313 g L −1 or 7.99 × 10 −2 mol/L (see ref. for calculation of the dye concentration).…”

Strong Coupling in Microcavity Structures: Principle, Design, and Practical Application

“…Light fields in microcavities can contribute to ≈20‐fold enhancement for low finesse cavities, up to as much as ≈400‐fold for high finesse cavities. Therefore, scattered and incident Raman scattering field effects can be enhanced, enhancing Raman cross sections several hundred folds compared to common effects …”