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arXiv:2001.04365 · Physical Review Letters

Phonon-Induced Optical Dephasing in Single Organic Molecules

Chloe Clear, Ross C. Schofield, Kyle D. Major, Jake Iles-Smith, Alex S. Clark, Dara P. S. McCutcheon

Published Apr 15, 2020• 51 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.124.153602

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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.
We continue the discussion of the nonperturbative theory of zero-phonon impurity lines in crystals formulated by Osad’ko and more recently by us. In that paper, a diagrammatic analysis was undertaken which led to analytic results for the thermal width and shift of the zero-phonon line. Here we evaluate these results for two model phonon densities of states: the Debye model for acoustic phonons, and a sharply peaked density of states appropriate for optical phonons. For Debye phonons we find that at low temperatures the standard (perturbative) theory of optical dephasing is qualitatively correct, but at high temperatures it becomes very inaccurate. Moreover, if one of the excited state phonon frequencies tends to zero (a soft mode), then perturbation theory breaks down completely. For optical phonons our results give an Arrhenius temperature dependence for the linewidth and place an upper bound on the value of the preexponential. In paper II of this series we will discuss dephasing by pseudo-local phonons, and in paper III we will compare our results to absorption, photon echo, and hole burning experiments.
We investigate the temperature dependence of photon coherence properties through two-photon interference (TPI) measurements from a single quantum dot (QD) under resonant excitation. We show that the loss of indistinguishability is related only to the electron-phonon coupling and is not affected by spectral diffusion. Through these measurements and a complementary microscopic theory, we identify two independent separate decoherence processes, both of which are associated with phonons. Below 10 K, we find that the relaxation of the vibrational lattice is the dominant contribution to the loss of TPI visibility. This process is non-Markovian in nature and corresponds to real phonon transitions resulting in a broad phonon sideband in the QD emission spectra. Above 10 K, virtual phonon transitions to higher lying excited states in the QD become the dominant dephasing mechanism, this leads to a broadening of the zero phonon line, and a corresponding rapid decay in the visibility. The microscopic theory we develop provides analytic expressions for the dephasing rates for both virtual phonon scattering and non-Markovian lattice relaxation.
An approximate excited state vibrational Hamiltonian, He, which accounts for both linear and diagonal quadratic electron-phonon coupling is derived and shown to be adequate for mode frequency changes up to ~30%. The associated linear response function which is valid for finite temperature in the absence of damping is obtained. 2-point correlation function or, equivalently, the line broadening function, g(t;T), that provides a good physical description of pure electronic dephasing and vibrational damping for linearly coupled modes is postulated. A linear response function that accounts for pure electronic dephasing and damping for systems with either linearly or quadratically coupled modes is proposed. Applications of the new linear response function include the single site absorption and hole-burned spectra of the special pair band of the bacterial reaction center and the temperature dependence of the single site absorption spectrum of Al-phthalocyanine tetrasulphonate in glassy ethanol. A 4-point correlation function which is valid for finite temperature in the absence of damping using the approximate excited state vibrational Hamiltonian, He, is derived. An impulsive stimulated photon echo signal for a single-mode system with very large inhomogeneous broadening is calculated using the 4-point correlation function. An expression for ordinary photon echo with two finite pulses is derived. 4-point correlation function for linearly coupled modes is expressed in terms of g(t;T) and can be used to calculate all non-linear spectroscopic signals. Applications of the 4-point correlation function are limited to impulsive 2-pulse photon echo (IPE) signals. IPE signals are generated for different values of the Huang-Rhys factor (S) at a fixed temperature and at different temperatures for a fixed value of S in order to see how the echo profile changes as one varies S or temperature. An initial fast non-exponential decay, which reflects the contribution of the phonon sideband, followed by vibrational oscillations (quantum beats) due to linear electron-phonon coupling and a slow exponential decay, on picosecond time scales, due to the zero-phonon line are observed in the IPE signals. Application of IPE to the special pair absorption band of the bacterial reaction center is also included.
We investigate temperature-dependent resonance fluorescence spectra obtained from a single self-assembled quantum dot. A decrease of the Mollow triplet sideband splitting is observed with increasing temperature, an effect we attribute to a phonon-induced renormalization of the driven dot Rabi frequency. We also present first evidence for a nonperturbative regime of phonon coupling, in which the expected linear increase in sideband linewidth as a function of temperature is canceled by the corresponding reduction in Rabi frequency. These results indicate that dephasing in semiconductor quantum dots may be less sensitive to changes in temperature than expected from a standard weak-coupling analysis of phonon effects.
The extraordinarily short optical dephasing time of organic dye molecules in polymer hosts is known to be under 20 fs between 100 and 200 K. Short dephasing times suggest enormously broadened homogeneous linewidths on the order of 10 nm. Direct observation of single dye molecule fluorescence spectra shows a similarly broadened line, giving comparable dephasing times for room temperature measurements. While this single molecule linewidth agrees with that of the bulk sample, it is inaccurate to attribute this broadening to homogeneous mechanisms. Repeated single molecule fluorescence measurements permit determination of the homogeneous nature of this linewidth, as distinct from the inhomogeneous nature of dispersion in bulk samples. Spectral diffusion in single molecule spectra is evidenced by multiple peaks, visible despite broad spectra lines at room temperature. In the particular experiment discussed in this thesis, fluorescence from single organic dye molecules in thin polymethyl methacrylate films was studied with scanning confocal microscopy. Photon antibunching exhibited by the photon-pair correlation function g(2) (τ) at τ = 0 confirms that single molecule emission spectra were obtained.
By using the zero-phonon line emission of an individual organic molecule, we realized a source of indistinguishable single photons in the near infrared. A Hong-Ou-Mandel interference experiment is performed and a two-photon coalescence probability higher than 5050%50 at 2 K is obtained. The contribution of the temperature-dependent dephasing processes to the two-photon interference contrast is studied. We show that the molecule delivers nearly ideal indistinguishable single photons at the lowest temperatures when the dephasing is nearly lifetime limited. This source is used to generate postselected polarization-entangled photon pairs as a test bench for applications in quantum information.