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The Journal of Physical Chemistry B

Four-Level Optical Line Shape of a Single Molecule Coupled to a Single Tunneling Two-Level System

Clemens Hofmann, Michel Orrit

Published Aug 11, 2006• 5 citations
Publisher

Abstract

We propose a density-matrix theory for the four-level system consisting of a single optical two-level system (OTLS) coupled to a single two-level system tunneling along a vibrational coordinate (VTLS). Phonons induce jumping rates of the VTLS, but coherent tunneling has to be considered explicitly as well, because the Born-Oppenheimer potential of the tunnel variable may change upon optical excitation. The OTLS is subject to spontaneous emission and driven by a laser wave with arbitrary strength. Numerical simulations for various coupling cases reproduce limiting behaviors previously discussed separately in the literature, such as motional narrowing, cross transitions, optical saturation and pumping, and nonlinear effects. Our model also perfectly fits recent measurements of the spectra of a single molecule coupled to a single tunneling system in a disordered crystal.

DOI
10.1021/jp0574908

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We propose a density-matrix theory for the four-level system consisting of a single optical two-level system (OTLS) coupled to a single two-level system tunneling along a vibrational coordinate (VTLS). Phonons induce jumping rates of the VTLS, but coherent tunneling has to be considered explicitly as well, because the Born-Oppenheimer potential of the tunnel variable may change upon optical excitation. The OTLS is subject to spontaneous emission and driven by a laser wave with arbitrary strength. Numerical simulations for various coupling cases reproduce limiting behaviors previously discussed separately in the literature, such as motional narrowing, cross transitions, optical saturation and pumping, and nonlinear effects. Our model also perfectly fits recent measurements of the spectra of a single molecule coupled to a single tunneling system in a disordered crystal.
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Stochastic dynamics of a laser-driven four-level system serving as a model for a single guest chromophore molecule in an amorphous polymer host is studied. The dynamics of ``slow'' transitions (spectral jumps), accompanied by instantaneous changes in the fluorescence frequency, is simulated on the basis of continuous measurement theory. It is shown that there is an opportunity to control the statistics of ``bright'' and ``dark'' periods by using laser fields to drive molecules having different tunneling rates for the ground and excited electronic states. The effect of population cycling in a four-level system and related effects of local heating or cooling of the environment are discussed.
A nonperturbative theoretical study of four-wave-mixing processes in four-level systems is presented. Using the density-matrix formalism, numerical results are obtained for two arbitrarily intense pump fields with the third field a weak probe. The fourth wave, radiated by the system, is obtained analytically for some special cases. We find, for different frequency detunings, Rabi frequencies, and relaxation rates that the line shapes exhibit: (i) dynamic Stark splitting and shifting, and merging of resonances; (ii) power broadening with two-photon antiresonance behavior resulting from a destructive interference between different contributions to the optical polarization; and (iii) extra resonances induced by field intensities and saturation processes.
We consider the Four-Wave mixing (FWM) signal and the effects of the pump beam on the nonlinear optical responses of a two-level system where intramolecular coupling is modelled by two coupled harmonic electronic potentials, displaced both in their equilibrium minimum position and energy. We investigate the modifications introduced in the FWM signal, considering a simple representation for the vibrational structure and including molecular electronic states with nonzero permanent dipole moments. The critical quantities for this analysis are the transition and permanent dipole moments, which depend strongly on the intramolecular coupling. Our results show how both absorption and dispersion are affected by the vibronic coupling.
Solid-state single organic molecules, such as dibenzoterrylene (DBT) in organic matrices, are prominent deterministic single-photon sources, usually modeled as effective two-level systems (TLS). We show that single DBT molecules in anthracene nanocrystals, under strong continuous-wave driving, depart from this picture: instead of the expected saturation, fluorescence is strongly suppressed at high resonant pump power, while the linewidth broadens beyond the TLS prediction -- an \emph{anomalous saturation} regime. Comparing coherent and incoherent excitation and independently calibrating temperature via phonon-induced dephasing rules out laser-induced heating and intersystem crossing. Instead, a model of intensity-dependent excited-state absorption (ESA) toward a short-lived dark state quantitatively reproduces both the fluorescence suppression and the linewidth broadening. We further show that matrix quality mitigates this quenching, and that pulsed excitation schemes are strategic toward full population inversion, with direct implications for quantum nanophotonics and molecular optomechanics.