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Physical Review Letters

Non-Lorentzian Single-Molecule Line Shape: Pseudolocal Phonons and Coherence Transfer

T. Nonn, Taras Plakhotnik

Published Aug 14, 2000• 16 citations
Publisher

Abstract

The excitation line shape of a single terrylene molecule in a naphthalene crystal has been investigated. In addition to the conventional Lorentzian, it consists of a dispersive component in the core region and a sideband. This is due to a pseudolocal phonon caused by the substitution of a host molecule with the chromophore. When the pseudolocal phonon is excited, the resonance frequency of the chromophore slightly changes, resulting in the appearance of a second, quasiresonant transition. Coherence transfer between these two optical transitions causes the deviation from the purely Lorentzian line shape.

DOI
10.1103/physrevlett.85.1556

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The excitation line shape of a single terrylene molecule in a naphthalene crystal has been investigated. In addition to the conventional Lorentzian, it consists of a dispersive component in the core region and a sideband. This is due to a pseudolocal phonon caused by the substitution of a host molecule with the chromophore. When the pseudolocal phonon is excited, the resonance frequency of the chromophore slightly changes, resulting in the appearance of a second, quasiresonant transition. Coherence transfer between these two optical transitions causes the deviation from the purely Lorentzian line shape.
Redfield relaxation theory is used to study optical dephasing in molecular mixed crystals where pseudolocalized phonons play a dominant role. As a model an effective four-level system is defined which consists of the ground and excited electronic state of the guest impurity and one pseudolocalized phonon in each of these states. It is shown that coherence transfer between the purely electronic and the phonon-promoted transition is due to interference between the scattering amplitudes in the ground and excited state and only occurs when the transitions are near resonant. When the scattering amplitudes in the ground and excited state are identical the optical Redfield equations reduce to the modified Bloch equations and coherence transfer may appreciably contribute to optical dephasing. It further proves essential for coherence exchange to occur that next to electron–phonon coupling the phonon anharmonicity is taken into account. The stochastic and correlation function theories of line shape, using the same model system, have also been examined and we conclude that in these theories exchange of coherence is not properly taken into account. Next to the effect of pseudolocalized phonons the effect of band phonons on optical dephasing is also examined and within our model both effects are additive.
The effects of different laser line shapes on the intensity and spectrum of resonance fluorescence from a two-level atom are investigated. The laser model considered is that of an ideal single-mode laser operating high above threshold, with constant amplitude and undergoing phase-frequency fluctuations analogous to Brownian motion. As the correlation time of the frequency fluctuations increases from zero to infinity, the laser line shape changes from Lorentzian to Gaussian in a continuous way. It is shown that for intermediate and strong fields, the average intensity of fluorescence in the case of a resonant broadband Lorentzian line shape is higher than that in the case of a Gaussian line shape with the same bandwidth and total power. This is in contrast to the weak-field case where the higher peak power of the Gaussian line shape makes it more effective than the Lorentzian line shape. It is also shown that in the case of a nonzero frequency correlation time (non-Lorentzian line shape) the intensity of fluorescence undergoes non-Markovian fluctuations. In relation to the spectrum of resonance fluorescence, it is shown that as the line shape is varied from Lorentzian to Gaussian the following changes take place: In the case of off-resonance excitation, the asymmetry of the spectrum decreases. In the case of resonant excitation, the center-peak to side-peak height ratio for the triplet structure increases. Moreover, the recently predicted center-line dip, which develops in the spectrum in the case of broadband excitation when the Rabi frequency and the bandwidth are nearly equal, becomes increasingly deeper.
The temperature-dependent optical dephasing of anthracene, 9-methylanthracene, and 2-methylanthracene monomers in phenanthrene host crystals has been measured using photon echo experiments. Despite large linear electron–acoustic phonon coupling, all three systems dephase because of coupling to pseudolocal modes (local motions of the guest molecule). Computer simulations of the three systems calculate the pseudolocal mode eigenvalues and eigenvectors. In contrast to previous discussions in the literature which describe pseudolocal modes as librations, the predicted eigenvalues are in reasonable agreement with the measured pseudolocal mode energies. The predicted eigenvectors are combinations of translational motion along the long molecular axis and rotational motion about the out-of-plane axis of the guest. Differences in site energies for various locations and orientations of the methyl group are calculated.
The interaction of an atomic system with a laser having phase fluctuations is studied within the phase-diffusion model, with the finite correlation time of the time derivative of the phase taken into account. This finite correlation time introduces a line shape which is Lorentzian near the center and falls off faster than the Lorentzian at its wings. The authors apply this model to calculate the spectrum of double optical resonance for excitation by a laser having this non-Lorentzian line shape. It is observed that the reversed peak asymmetry reverts to normal far off resonance owing to the cutoff of the laser spectrum, in agreement with recent experiments. Numerical results are presented.
We present a theoretical approach to describe the dynamics of a system induced by stochastic couplings and undergoing dephasing processes. We consider a model frequently encountered in the study of non-radiative transitions in molecular systems, the case of two configurations stochastically coupled. In this model, we use a system whose excited radiant state is coupled stochastically to a non-radiant state of a lower electronic configuration. We show the line shape for stochastic non-diagonal perturbations to remain Lorentzian. This result is different from the case of frequency modulation where a transition from a Gaussian to a Lorentzian line shape can be observed.
We present a joint experiment-theory analysis of the temperature-dependent emission spectra, zero-phonon linewidth, and second-order correlation function of light emitted from a single organic molecule. We observe spectra with a zero-phonon line together with several additional sharp peaks, broad phonon sidebands, and a strongly temperature dependent homogeneous broadening. Our model includes both localized vibrational modes of the molecule and a thermal phonon bath, which we include nonperturbatively, and is able to capture all observed features. For resonant driving we measure Rabi oscillations that become increasingly damped with temperature, which our model naturally reproduces. Our results constitute an essential characterization of the photon coherence of molecules, paving the way to their use in future quantum information applications.