Resonant Excitation Induced Vibronic Mollow Triplets

Abstract

The Mollow triplet is the definitive spectral signature of an optically dressed quantum emitter. We predict that for emitters coupled to localized phonons, this signature is not confined to the zero-phonon line. Under a strong resonant drive, we show that Mollow triplets are strikingly replicated on the associated phonon sidebands -a surprising result, given that phonon sidebands are typically viewed as incoherent, inelastic scattering pathways. These vibronic Mollow triplets are a direct fingerprint of dynamically generated dressed states that hybridize the emitter's electronic, photonic, and vibrational degrees of freedom. We develop a scalable analytical formalism to model this effect in complex, multi-mode molecular systems, such as dibenzoterrylene. Our work provides the precise driving conditions for observing these novel spectral features, establishing a new signature of coherence in vibronically coupled systems.

Figures (7)

• Figure 1: (a) Schematic of a two-level system driven by a CW laser and coupled to local phonon modes, forming an open quantum system that interacts with both photonic and acoustic phonon baths. (b) Coherence decay of an emitter coupled to a local phonon mode with $(\eta/\nu)^2= 0.25$ showing a rapid picosecond-scale drop (Inset) accompanied by visible Rabi oscillations. (c) Comparison of the Mollow triplet for $\eta = 0$ to $\eta = 1$. The parameters used are $\gamma = 4.1\;\mu\mathrm{eV}$, $\Omega = 10\gamma$, $\nu = 5$ meV and $\kappa = 0.2$ meV. (Inset) Mollow spectrum showing the triplet linewidths and amplitudes used to define the linewidth ratio $R_\Gamma = \Gamma_{\rm C}/\Gamma_{\rm S}$ and amplitude ratio $R_{\rm A} = A_{\rm S}/A_{\rm C}$.
• Figure 2: (a) Analytical spectra (normalized, log scale) of an emitter interacting with a single local phonon mode under varying driving strengths, revealing the emergence of vibronic Mollow triplets. The parameters used are $\nu = 5$ meV, $\eta = \nu/3$ meV and $\kappa = 0.2$ meV. (b) Transitions between dressed states explaining the appearance of Mollow triplets accompanied also by phonon generation resulting in not only the ZPL ($\delta n=0$), but also the first ($\delta n=1$) and second ($\delta n=2$) phonon sidebands. The diagram is not to scale, as the phonon energies exceed the Rabi splitting.
• Figure 3: (a) Normalized DBT spectrum from \ref{['eq:g1_gen']} at $T=8~\mathrm{K}$ shows ten fundamental modes (blue; red arrows mark peak positions by mode index) their higher-order overtones up to $n=3$ and sums of mode frequencies (in pink). Other simulation parameters are $\gamma = 0.094\;\text{µ}$eV and $\Omega = 10\gamma$. (b) Laser intensity (left $y$-axis) and its corresponding Rabi frequency (right $y$-axis) dependent lifetime limited DBT spectra for the first five fundamental local phonon modes, computed from \ref{['eq:DBT_ana']}. The bottom panel presents zoomed-in views of modes $j=1,3,4,5$. We use $\lambda = 745$ nm and the transition dipole moment as $d = 13.7D$ where $D =3.34\times 10^{-30}$ C-m Zirkelbach2022High-resolutionCrystal.
• Figure S1: (a) Temperature regime showing upto where one can use $N(\nu_j)\approx0$ for different DBT modes in para-dichlorobenzene given in Table. \ref{['tab:vibrational_modes_pCB']}. (b) $\Gamma$ vs temperature extracted from the analytical result of Clear2020Phonon.
• Figure S2: (a) Regime of validity the $8\Lambda_\alpha= 1$ approximation for $\Omega = 2\kappa_2$ (Table \ref{['tab:vibrational_modes_pCB']}) shown in the solid blue line (using Eq. \ref{['eq: Mollow_params']}) as a function of dephasing rate (bottom x-axis) and temperature (top x-axis) whose correspondence is shown in Fig. \ref{['fig:DBT_spectra_dephasing']}(b). The dashed blue line represents $8\Lambda_\alpha=1$. The solid red line depicts the normalized Mollow splitting (using Eq. \ref{['eq: Mollow_params']}) versus dephasing rate/temperature. The dotted vertical blue line marks $8\Lambda_\alpha=1.01$, to the left of which these quantities remain nearly constant. (b, c) Distinctively different characteristics of the Mollow triplets in ZPL and local phonon sidebands of a DBT molecule in pDCB (Table \ref{['tab:vibrational_modes_pCB']}) shown by temperature dependent variation of ratios of line broadening of the central and sidepeak ($R_\Gamma$) as well as their amplitude ratios ($R_{\rm A}$). In (b) the dashed colored lines represent the plots where the approximation $8\Lambda_\alpha = 1$ is used while the dashed black line represents $R_{\rm A} = 1$ below which the central peak will have lower amplitude than the sidepeaks.