Current experimental and theoretical progress toward the goal of controlling quantum dynamics is summarized. Two key developments have now revitalized the field. First, appropriate ultrafast laser pulse shaping capabilities have only recently become practical. Second, the introduction of engineering control concepts has put the required theoretical framework on a rigorous foundation. Extrapolations to determine what is realistically possible are presented.

https://science.sciencemag.org/content/sci/259/5101/1581.full.pdf

Coherent control of quantum dynamics: the dream is alive.

Recent advances in fluorescence excitation spectroscopy with high efficiency have produced greatly improved optical spectra for the first electronic transition of individual single molecules of pentacene in p‐terphenyl crystals at low temperatures (1.5 to 10 K). Two classes of single molecule behavior are observed: class I molecules have time‐independent resonance frequencies, and class II molecules show a diffusive motion among several resonant frequencies with time which we term ‘‘spectral diffusion’’ by analogy with a similar effect which is common in amorphous materials. The temperature dependence of the linewidth and the power dependence of the fluorescence emission rate and of the linewidth are reported and analyzed. Various forms of the surprising class II behavior are described, including jumping among several discrete frequencies, creeping toward the center of the inhomogeneous line in many small steps, and a wandering among many possible resonance frequencies. The occurrence of class II behavior is restricted to the wings of the inhomogeneous line suggesting that the effect is correlated with some form of local disorder. The spectral diffusion rate increases with increasing temperature, suggesting that the effect may be due to phonon‐assisted transitions of local degrees of freedom around the pentacene defect whose source remains to be identified conclusively.

Detection and spectroscopy of single pentacene molecules in a p‐terphenyl crystal by means of fluorescence excitation

▪ Abstract Recent experimental and theoretical studies concerning single-molecule spectroscopy in solids are discussed. Pure quantum effects—such as photon bunching, antibunching, and spectral jumps—and more classical phenomena—such as near-field excitation, saturation, ac/dc Stark shifts, spectral diffusion, two-photon excitation, and customary spectroscopic analysis—are considered. The emphasis of this review is on physical results and their interpretation. This is preceded by a general introduction, where fundamentals of single-molecule spectroscopy are explained.

Single-molecule spectroscopy

Fluorescence photons emitted by a single molecule trapped in a solid at low temperature are correlated in time. A simple theory of the correlation pattern is presented, including in the same formalism photon antibunching from coherent Rabi oscillations and photon bunching due to incoherent quantum transitions between electronic levels. The correlation method is applied to single pentacene molecules in a para‐terphenyl crystal. A clear photon bunching allows us to determine the ISC rates for each molecule. We attribute the scatter of our results for the transition rate between excited singlet and triplet states, and the difference with the average value taken from the literature, to molecular distortions induced by crystal defects in our small sample. We conclude that the correlation method associated to single molecule spectroscopy has a great potential to study dynamical processes on intermediate time scales in condensed matter.

Photon bunching in the fluorescence from single molecules: A probe for intersystem crossing

The initial steps toward optical detection and spectroscopy of single molecules in condensed matter arose out of the study of inhomogeneously broadened optical absorption profiles of molecular impurities in solids at low temperatures. Spectral signatures relating to the fluctuations of the number of molecules in resonance led to the attainment of the single-molecule limit in 1989 using frequency-modulation laser spectroscopy. In the early 90s, many fascinating physical effects were observed for individual molecules, and the imaging of single molecules as well as observations of spectral diffusion, optical switching and the ability to select different single molecules in the same focal volume simply by tuning the pumping laser frequency provided important forerunners of the later super-resolution microscopy with single molecules. In the room temperature regime, imaging of single copies of the green fluorescent protein also uncovered surprises, especially the blinking and photoinduced recovery of emitters, which stimulated further development of photoswitchable fluorescent protein labels. Because each single fluorophore acts a light source roughly 1 nm in size, microscopic observation and localization of individual fluorophores is a key ingredient to imaging beyond the optical diffraction limit. Combining this with active control of the number of emitting molecules in the pumped volume led to the super-resolution imaging of Eric Betzig and others, a new frontier for optical microscopy beyond the diffraction limit. The background leading up to these observations is described and current developments are summarized.

Single‐Molecule Spectroscopy, Imaging, and Photocontrol: Foundations for Super‐Resolution Microscopy (Nobel Lecture)

One purpose of this paper is to present new studies on the effect of bandwidth and the coherence properties of the excitation source on the decay and the dephasing of isolated large molecules. A detailed study of the system pentacene in a p-terphenyl matrix is presented utilizing three different excitation sources, a single mode dye laser (60 KHz–6 MHz bandwidth depending on the time scale of the experiment) a multimode dye laser (240 GHz bandwidth), and an incoherent N2 flash lamp. Optical T1 (the longitudinal relaxation time) and T2 (the transverse relaxation time) are measured from the coherent and incoherent transients observed either in the forward direction of the laser or at right angles to the exciting beam. At 1.8 °K, the optical transition (1A1g-->1B2u) of pentacene in p-terphenyl exhibits four sites, the lowest of which at 16 887 cm−1 has the following parameters: T2=44±2 nsec; T1=24.9±2 nsec, and µ=0.7±0.1 D. The transition moment µ, is obtained directly from the optical nutation, which exhibits a Rabi nutation time (h-slash/µ·epsilon) of 27.3 nsec, and is corrected for the effect of the Lorentz local field inside the terphenyl crystal. The experiments presented here are categorized into two time regimes for theoretical analysis; a transient coherence regime where the observed decay is comparable with (h-slash/µ·epsilon) and T2, and a steady-state coherence regime where transient dephasing is complete and the off-diagonal elements of the density matrix have decayed to their steady-state values in the presence of the field of amplitude epsilon. Using the Wilcox–Lamb method, rate equations (with T2 expressions) describing the population flow in the ''complete'' level structure of pentacene (ground||0>, singlet ||p>, and triplet {||l}) are derived from the density matrix equations of motion. When these equations are averaged over the inhomogeneous width of the optical transition and the measured Gaussian transverse profile of our laser we obtain T1p0=24.9±2 nsec and T1pl=15.7 µsec, the time constants by which pentacene spontaneously decays to ||0> or crosses over into l, as well as the averaged population at time t. In an effort to be complete, attention is placed upon the relationship between theory and the experimental findings. First, expressions for the OFID and nutation in the solid are presented for the pentacene case in order to relate T1, T2, and µ to the level structure. Second, at low temperatures (1.8 °K), the origin of dephasing is identified as spontaneous emission from p-->0 since experimentally T2?2T1, in agreement with other work. At higher temperature, however, a strongly temperature dependent dephasing process with an onset at 3.7 °K takes place. Armed with these observations we present a theoretical treatment of these distinct dephasing channels and their temperature dependences. A discussion regarding the influence of ''accepting'' phonon modes (either optical or acoustic) on optical dephasing is also given. The results indicate that the treatment of Jones et al. can (1) explain the observed temperature dependence of T2 in pentacene; (2) distinguish dephasing as a result of scattering by acoustic phonons from that due to resonance or quasilocalized phonons with clear connections to gas and liquid state theories, but without invoking more than two approximation levels. (3) explain both the level shift and line width changes as a result of ''conventional'' dephasing or dephasing by exchange mechanisms; and (4) relate the pure dephasing term to an anisotropy in the scattering amplitudes (between the ground and excited states in the system) which contribute largely to the homogeneous width of the transition. Optical site selection of these transitions is also reported and discussed in relation to vibrational relaxation and to both homogeneous and inhomogeneous broadenings. The studies of the homogeneous broadening of the vibronic origin (267 cm−1) indicate that vibrational relaxation is fast (psec) in the excited singlet manifold of pentacene. Finally from more than ten independent experiments including single and multimode excitation, on- and off-resonance scattering, Zeeman effect and the transient decay as a function of excess energy in the molecule, a more complete picture of the pentacene level structure {||l>} is given. With this in mind, the influence of the laser bandwidth and coherence properties on state preparation and subsequent dephasing and decay is concluded. It is proposed that the slow decay, (~15 µsec) observed during narrow-band excitation represents intersystem crossing to nearby triple manifolds after the transient coherence of the 0 p subsystem is decayed. In addition, the decay of the primary state prepared in these experiments is not sensitive to the bandwidth or the correlation time of our excitation sources.

/pdf/radiationless-relaxation-and-optical-dephasing-of-molecules-2cxwewndu2.pdf

T. E. Orlowski

Papers

Radiationless relaxation and optical dephasing of molecules excited by wide- and narrow-band lasers. II. Pentacene in low-temperature mixed crystals