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The Journal of Physical Chemistry B

Molecular Binoculars: How to Spatially Resolve Environmental Fluctuations by Following Two or More Single-Molecule Spectral Trails at a Time

Vassiliy Lubchenko, R. Silbey

Published Apr 23, 2013• 1 citation
Publisher

Abstract

We propose a novel type of spectral diffusion experiment that enables one to decouple spatial characteristics of the environmental fluctuations, such as their concentration, from the interaction with the chromophore. Traditional hole broadening experiments do not allow for such decoupling in the common case when the chromophore-environment interaction is scale invariant. Here we propose to simultaneously follow the spectral trails of a small number of nearby chromophores--two or more--which thereby sense a highly overlapping set of the fluctuations. To this end, we estimate the combined probability distribution for the frequencies of a set of chromophores contained within the same sample. The present setup introduces a new length scale, i.e., the interchromophore distance, which breaks the aforementioned scale invariance and enables one to determine independently the concentration of the environmental fluctuations and their coupling to the chromophores, by monitoring the time after which spectral diffusion of distinct chromophores becomes uncorrelated. We illustrate these results with structural excitations in low temperature glasses.

DOI
10.1021/jp401085p

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We propose a novel type of spectral diffusion experiment that enables one to decouple spatial characteristics of the environmental fluctuations, such as their concentration, from the interaction with the chromophore. Traditional hole broadening experiments do not allow for such decoupling in the common case when the chromophore-environment interaction is scale invariant. Here we propose to simultaneously follow the spectral trails of a small number of nearby chromophores--two or more--which thereby sense a highly overlapping set of the fluctuations. To this end, we estimate the combined probability distribution for the frequencies of a set of chromophores contained within the same sample. The present setup introduces a new length scale, i.e., the interchromophore distance, which breaks the aforementioned scale invariance and enables one to determine independently the concentration of the environmental fluctuations and their coupling to the chromophores, by monitoring the time after which spectral diffusion of distinct chromophores becomes uncorrelated. We illustrate these results with structural excitations in low temperature glasses.
We develop a systematic description of spectral diffusion of ideal chromophores interacting with incoherently relaxing two-state, localized environmental degrees of freedom ("spins") for general initial environment configurations. We remedy the existing, incomplete treatments by formulating the problem in terms of the proper correlation function and by obtaining an accurate solution for generic aperiodic arrangements of environmental spins, nearly free of the customary simplifying assumptions on the multiparticle spin coordinate distribution. We report and estimate, for the first time, the effects of the drift and distortion of a narrow spectral line that arise when the line is not in the center of the inhomogeneous band. While the drift turns out to be modest in most ensemble measurements, accounting for its effects is imperative in analyzing single chromophore spectral jumps, to which end the authors propose a novel experiment. Further, we argue that by employing a sufficiently large chromophore one can decouple the concentration of the fluctuating centers from the strength of their interaction with the chromophore. Finally, the additional line broadening, owing to a distribution of the central chromophore frequencies, is evaluated. Upper estimates for an analogous broadening stemming from a nonequilibrium environment are made.
We consider the spectral diffusion of a chromophore coupled through dipolar interactions to a regular lattice of flipping two-level systems. In particular, we calculate the spectral diffusion kernel, P(ω,t‖ω0), which is the conditional probability density that the chromophore will have transition frequency ω at time t, given that it had frequency ω0 at time 0. At very short times we find that the spectral diffusion kernel is Lorentzian, for any value of the two-level system excitation probability, p. For longer times the form of the spectral diffusion kernel depends on the value of p. We derive several approximate expressions for the spectral diffusion kernel, all of which go to the correct equilibrium distribution of frequencies for long times. For p≂1/2, when the frequency distribution is nearly Gaussian, we find that the spectral diffusion kernel is not at all Gaussian for short times. We compare all of our approximate expressions with numerically exact results. Motivated by certain optical spectral diffusion experiments on individual molecules in solids, we also calculate P(Δ;t), the distribution of spectral jumps, which is the probability density that the chromophore’s frequency will change by an amount Δ in time t. In a subsequent paper we will analyze these spectral diffusion experiments with our results.
Picosecond photon echo (PE) experiments are used to examine the optical dephasing and intermolecular interactions of organic chromophores in a variety of glassy organic and polymer hosts. The inherent disorder in these systems leads to dynamics which span times from picoseconds to hours and longer. The temperature dependent optical dephasing as measured by the PE follows a power law characteristic of tunnelling twolevel systems (TLS) at low temperatures (1 °K to 4 °K) and is exponentially activated at higher temperatures due to dephasing by additional modes. The nature of these modes will be addressed. These data and those from other line narrowing experiments such as hole burning allow the study both of fast dephasing processes and spectral diffusion due to slow fluctuations in the host. The observed lineshapes and holewidths require dipolar coupling between the chromophore and TLS and offer information on the distribution of relaxation rates. Furthermore, techniques sensitive to different timescales are used to examine host dynamics by removing the guest-host coupling from consideration. The data are discussed in conjunction with recently developed theoretical treatments of dephasing in disordered systems.
A framework for calculating photon emission statistics for single chromophores perturbed by slow environmental fluctuations is introduced. When internal chromophore dynamics are significantly faster than time scales for environmental modulation it becomes possible to invoke a type of adiabatic approximation, allowing for straightforward calculation of photon counting moments including explicitly quantum effects. Unlike previous exact treatments, the present methodology involves calculation of dynamics reflecting only the modulation characteristics of the environment and quantum dynamics of an isolated chromophore separately, i.e., the complicated intermingling of chromophore quantum dynamics and the environmental modulation are suppressed via the adiabatic approximation. This leads to significant conceptual and computational simplifications. Within its regime of applicability, the present approximation reproduces exact calculations quantitatively. We demonstrate this accuracy explicitly for the case of a two-level chromophore modulated by a number of different stochastic models.
The photon echo (PE) spectroscopy and single-molecule spectroscopy (SMS) may be combined to give a very powerful tool for comprehensive study of low-temperature dynamics in dye-doped disordered solids (polymers, glasses). At the same time, this type of studies are likely to reveal discrepancies when comparing characteristic times of optical dephasing T2 and single-molecule zero-phonon spectral lines (ZPL) broadening obtained from PE and SMS, correspondingly, for tetra-tert-butylterrylene in polyisobutylene in the temperature range of a few–dozen of Kelvins [see Phys. Status Solidi B 241, 3480 and 3487 (2004)]. Inexplicably, PE-experiments demonstrated T2-times to be much shorter than it is sufficient to cause the corresponding ZPL broadening. Here we experimentally solve this problem and show that at T = 4.5–15 K the incoherent PE gives T2-times which correspond to the narrowest SM ZPL. On the SM-level there is a pronounced additional ZPL-broadening due to spectral diffusion processes which are strongly dependent on the characteristics time of the measurement (tens of nanoseconds for PE and seconds for SMS). There is also a broad distribution of ZPL spectral widths for different SMs due to different local environments, that contribute differently to both the optical dephasing and the spectral diffusion processes, but always in addition to the value of inverse optical dephasing times measured using a PE technique.
By severely reducing the number of solute molecules in the illuminated sample, the optical resonances of individual molecules can be resolved in a fluorescence excitation spectrum. Single molecule lines can be studied as a function of time and temperature: sudden jumps of their resonance frequencies are due to spectral diffusion processes. The signal from a single molecule displays specific correlations which makes time-resolved studies possible. Here, emphasis is put on photon-bunching arising from intersystem crossing (ISC). ISC rates are deduced from the observed decay rates of the correlation and are found to differ from molecule to molecule. A single molecule is a truly local probe of its environment by means of which fundamental studies of the matrix dynamics as well as nanophysics experiments may be undertaken.