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Abstract
Single-molecule spectroscopy has been extensively used to investigate heterogeneity in static and dynamic behaviors on millisecond and second timescales. More recently, single-molecule pump-probe spectroscopy emerged as a method to access heterogeneity on the femtosecond and picosecond timescales. Here, we develop a single-molecule pump-probe apparatus that is easily tunable across the visible region and demonstrate its utility on the widely-used fluorescent dye, Atto647N. A spectrally-independent, bimodal distribution of energetic relaxation time constants is found, where one peak corresponds to electronic dephasing (∼ 100 fs) and the other to intravibrational relaxation (∼ 300 fs). The bimodal nature indicates that relaxation within each individual molecule is dominated by only one of these processes. Both peaks of the distribution are narrow, suggesting little heterogeneity is present for either process. As illustrated here, spectrally-tunable single-molecule pump-probe spectroscopy will enable investigation of the heterogeneity in a wide range of biological and material systems.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Ensemble transient absorption spectroscopies are routinely used to explore the excited-state dynamics in a wide range of condensed phase systems [1–7]. Analysis and separation of the contributions to spectral broadening in ensemble measurements have established that the presence of nano-environments within these systems give rise to the sub-populations, which collectively determine the material properties [8,9]. With the advent of single-molecule spectroscopy, these sub-populations have been explored directly, and photophysical heterogeneity has been observed [2,10–12]. However, traditional single-molecule techniques lacked the femtosecond temporal resolution required to investigate the heterogeneity in the excited-state dynamics.
In recent years, a suite of new techniques has appeared to probe femtosecond dynamics for sub-populations. Transient absorption microscopy interrogates micron-scale regions of a sample or a single nanostructure [1–6]. While these methods have revealed heterogeneity in solid materials such as graphene or perovskites [3–6,13], transient absorption measurements rely on a nonlinear signal, and so the region interrogated must produce large signals and be highly photostable [2]. As a result, these techniques have not been used on single molecules or proteins. Single-molecule pump-probe spectroscopy (SM2P) is an alternative approach that modulates the fluorescence emission to access femtosecond dynamics of single fluorescent particles. SM2P incorporates two ultrafast excitation pulses into a single-molecule confocal microscope and the level of fluorescence emission depends on the delay between the pulses [14–16]. This technique has been used to investigate vibrational relaxation and to coherently control excited state populations in single pigments and to observe coherent wavepacket oscillations and characterize energetic relaxation in photosynthetic light-harvesting complexes [17–19]. SM2P, therefore, has the sensitivity required to investigate molecules and proteins at the single-molecule level.
Herein, we introduce a spectrally tunable version of SM2P that allows facile exploration of excited-state dynamics across the visible range. Whereas previous SM2P apparatuses were tuned via the Ti:Sapphire gain curve, the introduction of a fiber laser extends the measurement down to 450 nm, spanning the visible region of the spectrum. Furthermore, the simple turn-key operation of the fiber laser combined with the incorporation of single-prism compression enables easy alignment. We demonstrate the utility of the apparatus on the widely-used single-molecule dye, Atto647N, and observe spectrally-independent energetic relaxation. A bimodal distribution of relaxation time constants is observed, which shows two processes are present on the timescales interrogated and that relaxation in an individual molecule is dominated by one of these processes. We assign the two peaks to electronic dephasing on a 100 fs timescale and intravibrational relaxation on a 300 fs timescale, based on previous work [14–16]. Both peaks are narrow, which indicates little molecule-to-molecule variation likely due to the homogeneity of the solution-phase environment. Detailed simulations of SM2P data characterized the influence of Poissonian noise the measured distributions. Collectively, these results determined the heterogeneity in energetic relaxation for Atto647N, and laid the groundwork for studies of the spectral dependence of heterogeneity in material and biological systems across the visible region.
2. Single-molecule pump-probe (SM2P) spectroscopy
SM2P relies on an isoenergetic 2 pulse pump-probe like excitation in the saturating regime where the laser is exclusively resonant with a higher-lying excited state [14,15,19]. As shown in Fig. 1(A) and (B), the sample can be modeled as a three-level system where the first saturating pulse generates damped Rabi oscillations between the ground state and higher-lying excited state that, in the long-time limit of our pulse duration ($\sim$100 fs), is equilibrated to the same probability of the molecule being in either state. As the delay increases, the population in the higher-lying excited state increasingly relaxes to the off-resonant state. The second pulse then re-equilibrates the population remaining in the higher-lying state with that in the ground state, which increases the probability of population for a depleted higher-lying state. Due to its narrow bandwidth, the pulse does not interact with the off-resonant state. The re-equilibrated population of the higher-lying excited state continues to undergo relaxation into the off-resonant state, from which it eventually fluoresces on a nanosecond timescale. Due to the proportionality between the population of the off-resonant state and the detected fluorescence, when the delay is scanned from negative to positive delay times, a dip-like shape is seen in the fluorescence emission (Fig. 1(C)), which can be fit to extract the time constant of relaxation from the higher-lying excited state to the off-resonant state.
Fig. 1. (A) Excitation pulse sequence in SM2P, where the pump and probe pulses are separated by a time delay, $\Delta T$. (B) Jablonski diagrams of the ground state, |0$\rangle$, and two excited states (higher-lying state, |1$\rangle$ lower-lying state, |2$\rangle$). The excitation undergoes energetic relaxation from |2$\rangle$ to |1$\rangle$ with a timescale, $\tau _{ER}$. (C) When $\Delta T$ is less than $\tau _{ER}$, the probe pulse stimulates emission, decreasing the fluorescence intensity (left). When $\Delta T$ is greater than $\tau _{ER}$, the probe pulse arrives after the excitation has relaxed to |2$\rangle$, and the excitation can be emitted as fluorescence (right). (C) A scan of $\Delta T$ from negative to positive produces a dip-like shape where the width of the modulation is governed by $\tau _{ER}$. Simulated data including Poissonian noise is shown in gray.
2.1 Experimental setup
A schematic of the experimental setup is shown in Fig. 2(A). A tunable fiber laser (FemtoFiber pro, Toptica; $\sim$100 fs pulse duration, $\sim$4 nm bandwidth, 80 MHz repetition rate) that spans the visible spectrum was used for the experiment. Due to the high powers required for saturating excitation, the single chromophores quickly photobleached, which appeared as a permanent reduction of the fluorescent intensity to the background level (40 Hz). To reduce the effects of photobleaching, the laser repetition rate was reduced from 80 MHz to 312.5 kHz with an acousto-optic pulse picker (Brimrose Corporation, FSPP-400-80-BR-800). The selected repetition rate was the lowest available with the pulse picker, which led to the longest period before photobleaching.
Fig. 2. (A) Schematic of the apparatus shows the femtosecond fiber laser excitation source focused and collimated by a set of parabolic mirrors (PM) into an acousto-optic modulator (AOM), which is used as a pulse picker to reduce the repetition rate. The pulse is compressed by a single-axis prism compressor paired with two retroreflectors (RR1 and RR2) before traveling through a set of beam splitters (BS) and a delay stage in a Mach-Zehnder configuration. The horizontal polarization is converted to right handed polarization by a quarter-waveplate ($1/4 \lambda$) before being focused to a diffraction limited spot by the objective. The emission is collected through the same objective, filtered by a dichroic mirror (DM) to remove the excitation light, and focused onto a single-photon avalanche photodiode (APD). The dashed green line shows an optional path with another BS and a more precise delay stage (Newport Picomotor Actuator Model 8302 with stage Model 9067-COM-E, minimum step size: 80 nm) introduced using removable magnetic mirror mounts (MM1 and MM2) to record the interferometric autocorrelation. (B) Schematic of the single-axis prism compressor for facile compression. (C) Representative interferometric autocorrelation (left panel) measured at the sample position with the extracted intensity autocorrelation (right panel, FWHM = 118 fs). The red line shows a fit assuming a Gaussian pulse.
A single-axis prism compressor, illustrated in Fig. 2(B), was set to minimize dispersion effects from the high NA objective at the sample position [20], which allows straightforward optimization of the compression for different wavelengths. The pulse duration was measured by interferometric autocorrelation using a GaP photodiode (Marktech, MTPD3650D-1.4) at the sample position [21,22]. The dashed green lines in Fig. 2(C) show the optical path for the autocorrelation measurements. To achieve the step size required for interferometric measurements in the visible region, the autocorrelation was performed with a dedicated translation stage (Newport Picomotor Actuator Model 8302 with stage Model 9067-COM-E, minimum step size: 80 nm). The differential dispersion in the two arms due to the beamsplitter (Thorlabs, UFBS5050) was neglected because it only adds $\sim$500 fs2 of group delay dispersion at 610 nm. The additional dispersion would extend a pulse of 100 fs to 101 fs, which can be ignored for the reported measurements. A representative intensity autocorrelation is shown in Fig. 2(C) where a full width at half maximum (FWHM) of 118 fs was extracted assuming a Gaussian pulse. Replicate autocorrelation measurements found 95% confidence intervals to be within $\sim$10% of the mean value.
The laser pulses were split by a set of beamsplitters (Thorlabs, UFBS5050) and a delay stage (Newport ISL100CC, minimum step size: 1 $\mu$m) in a Mach-Zehnder interferometer. To prevent dipole orientation dynamics from affecting the experiment, the laser exication was converted to circular polarization using a zeroth order quarter-waveplate (Newlight Photonics, WPM03-Q-VIS). The pulse pairs were coupled into an inverted confocal microscope (Mad City Labs, Stage Model Nano-LP100) and focused onto the sample with an objective (UPLSAPO100XO, Olympus, NA 1.4). Emission was isolated through the combination of a dichroic mirror determined by excitation wavelength (Chroma, T635lpxr-UF3; Chroma, ZT647rdc-UF2)) and two bandpass filters (Semrock, FF02-675/67-25; Chroma, ET690/120x). An avalanche photodiode (SPCM-AQRH-15, Excelitas) with a time-correlated single photon counting module (TimeTagger20, Swabian Instruments) was used to detect the fluorescence photons and had an instrument response function of $\sim$0.5 ns for fluorescence lifetime experiments.
Atto647N (ThermoFisher, 04507-1MG-F) was initially diluted in DMSO and then diluted in water to a final concentration of $\sim$ 500 pM in solution that was 1% polyvinyl alchohol. An enzymatic oxygen-scavenging system was added to the solution at final concentrations of 25 nM protocatechuate-3,4-dioxygenase and 2.5 mM protocatechuic acid [23,24]. 50 $\mu$L of the solution was spin-coated onto glass coverslips. This concentration gave rise to about one molecule per square micron.
For SM2P experiments the power was set to $\sim$1 pJ per pulse at the sample plane. The center wavelength of the laser was tuned to either 610 nm or 645 nm with a focal spot FWHM of $\sim$350 nm at the sample plane. For the 610 nm measurements, experiments were performed with near-transform limited temporal compression (118 fs). For the 645 nm measurements, experiments were performed with no temporal compression (300 fs) due to power limitations via bypassing the prism compressor. The delay time between pulse pairs was scanned from −1.5 ps to 1.5 ps at 100 $\mu$m/s ($\sim$300 ps/s). Although the FWHM of the 645 nm pulse was 300 fs, theoretical work has shown that the strong interaction in the presence of saturating laser pulses improves the temporal resolution [25–27]. For example, previous SM2P measurements recovered timescales as short as one sixth of the FWHM [19].
Fluorescence emission was binned at 50 ms intervals, which gives a data point every $\sim$30 fs. Photobleaching appears as a permanent reduction of fluorescence intensity down to background levels. Analysis was limited to molecules that photobleached after completion of the full SM2P trace ($\sim$4 s). Single molecules also exhibit fluorescence intermittency and blinking due to local conformational and environmental changes [28–30]. Intermittency appears as a change in the fluorescence intensity and molecules that exhibited intermittency were removed from further analysis. Blinking appears as a brief (<50 ms) reduction of the intensity down to background levels. The time point corresponding to the blinking event was not included in the fitted data, i.e., points identified as blinking events did not contribute to the error function that was minimized to extract relevant timescales. A blinking event was observed in $\sim$10% of molecules. The binned data was fit to the convolution of the measured intensity autocorrelation with an exponential rise [19]. A small fraction ($\sim$5%) of SM2P traces were collected on a previously-measured molecule, but the fraction was not sufficient for statistically robust independent analysis.
2.2 Simulations of SM2P data
To aid in the interpretation of SM2P data, simulated traces were generated in MATLAB. A simple three-level system was used as shown in Fig. 1(A) and 1(B). In the saturating limit and where the pulses are longer than the dephasing time, the population of the states in the three-level system can be described by the following differential equations [14,15,19]:
Where $N_0$, $N_1$, and $N_2$ are the population of $|{0}\rangle$, $|{1}\rangle$, and $|{2}\rangle$, respectively, $k_L$ is the rate of absorption/stimulated emission, $k_f$ is rate of fluorescence, and $k_{ER}$, i.e. $\frac {1}{\tau _{ER}}$, is the rate of energetic relaxation. Note that $k_f \approx 0$ because fluorescence occurs on a much longer timescale (ns) than energy redistribution and $k_L = \alpha I(t,\Delta$T$)$ where $\alpha$ is the absorption cross section and $I(t,\Delta$T$)$ is the intensity profile of the two pulse laser excitation with time delay $\Delta$T. In practice, the pulsed excitation was modeled as a Gaussian with a FWHM of 150 fs and the amplitude of the Gaussian pulses were set to one. $k_L$ was then increased by varying $\alpha$ until saturation was obtained, which was determined by monitoring the value at which the probability of $N_1$ became 50% under a single pulse excitation. For a specific time delay ($\Delta$T), Eqs. (1)–(3) are numerically integrated to simulate system dynamics observed through the population of $N_2$, which is directly proportional to the observed fluorescence. By controlling the time delay between the excitation pulses, we generate a fluorescence curve comparable to the one obtained experimentally and the fit function was used to extract the simulated time constants.The finite photon budget of a single molecule limits the signal-to-noise ratio (SNR) of SM2P data. The observed fluorescence intensity (Ifl) of our SM2P experiments is $\sim$100 photons$/$50 ms. The theoretical modulation depth of 33% [15,19] means that the signal is $\sim$33 photons$/$50 ms. Due to the stability of the laser and microscope, the dominating contribution to noise is Poissonian fluctuations in the number of detected photons, given by $\sigma_{\textrm{fl}}=\sqrt {\textrm{I}_{\textrm{fl}}}=$10 photons$/$50 ms. Collectively, these values yield a SNR of $\sim 3:1$. Although the SNR could be improved with further averaging, the acquisition time is limited by rapid photobleaching due to the saturating power used in our experiment.
The ability to extract the underlying parameters was investigated by simulating traces with typical levels of Poissonian noise and fitting them in the same manner as the experimental data to extract energetic relaxation time constants. Representative simulated traces for a $\tau _{ER, \textrm{sim}}$ of 250 fs are shown with their fit values in Fig. 3. The presence of Poissonian noise can distort the fit, which, as illustrated here, gives rise to variation in the extracted time constants. To quantify the variation, the simulation was repeated 100 times for a range of energetic relaxation time constants. First, single time constants of $\tau _{ER, \textrm{sim}}$ = 150 fs, $\tau _{ER, \textrm{sim}}$ = 250 fs, and $\tau _{ER, \textrm{sim}}$ = 500 fs were investigated. These time constants were selected to span the pulse duration (150 fs) to the energetic relaxation time constants (500 fs) observed in molecular systems [31]. For each time constant, histograms were constructed from the values extracted by fitting the simulated traces (Fig. 4(A–C)). The medians of the histograms recovered the time constants with relatively high fidelity. The histograms had standard deviations of $\sim$100–200 fs and little dependence on the value of the time constant itself was observed in this regime (7 fs per 100 fs; Supplement 1, Fig. S1). These standard deviations reflect narrow distributions as expected for single time constant simulations.
Fig. 3. Simulated SM2P traces. Representative traces with an input of $\tau _{ER, \textrm{sim}}$ = 250 fs where the $\tau _{ER}$ extracted from the fit is shown above. Variation from the input time constant is introduced by Poissonian noise.
Fig. 4. Distribution of energetic relaxation time constants for simulated SM2P traces. SM2P experiments were simulated using the input values plotted in blue of single time constants of 150 fs (A), 250 fs (B), and 500 fs (C); Gaussian distributions (dashed) around a center time constants of 250 fs with standard deviations of 25 fs (D), 100 fs (E), and 400 fs (F); two time constants with equal amplitude of 150 fs and 500 fs (G), 250 fs and 500 fs (H), and 350 fs and 500 fs (I); and for two time constants of 150 fs and 500 fs with amplitudes of 70% and 30% (J), 30% and 70% (K) and 10% and 90% (L). The extracted parameters from the distribution are shown in the upper right corner of each panel and listed in Table S1 in Supplement 1.
To investigate the ability of SM2P to characterize the distribution of behaviors, simulations were performed for single time constants randomly drawn from a Gaussian distribution. Specifically, a fixed central value of $\tau _{ER, \textrm{sim}}$ = 250 fs was used with $\sigma _{sim}$ values of 25, 100, and 400 fs. Histograms of the resulting simulations are shown in Fig. 4(D)–(F). For distributions narrower than the $\sim$125 fs width from Poissonian noise alone (Fig. 4(D) and (E)), the width remains similar and no additional information is extracted. For distributions wider than the width from Poissonian noise (Fig. 4(F)), both the median and the width are affected.
Lastly, to investigate the ability of SM2P to extract multiple time constants, simulations were performed for two components. The timescale was randomly selected from two Gaussian distributions with the specified mean values and a standard deviation of 25 fs for each one. Figure 4(G)–(I) shows the influence of the presence of two components with equal amplitudes on the distribution. The extracted median value is an accurate average of the two time constants. With a 350 fs and 250 fs separation (Fig. 4(G) and (H), respectively), the bimodal nature of the distribution is clear. However, for a 150 fs separation, the two time constants are too close to resolve, and the distribution is similar to one for a single time constant (e.g., Fig. 4(C)), with the median shifted towards slightly shorter values. Collectively, these results suggest that multiple components closer than 150 fs cannot be resolved, while those further apart could be separable, depending on the heterogeneity in the time constants themselves.
Figure 4(J)–(L) shows the influence of the presence of two components with varying amplitudes on the distribution for time constants with a 350 fs separation. When the two components had amplitudes of 70%/30% (Fig. 4(J) and (K)), the distribution appeared asymmetric, although with significant population at both timescales. However, for amplitudes of 90%/10% (Fig. 4(L)), the distribution peaked around the dominant timescale, and it would be difficult to reliably extract information about the minor component.
3. Energetic relaxation in Atto647N
We used SM2P to investigate ultrafast excited-state relaxation in Atto647N, a photostable fluorophore widely used in single-molecule imaging. The absorption and fluorescence spectra of Atto647N are shown in Fig. 5(A) along with the laser spectra. Excitation at 610 nm and 645 nm was chosen to isolate the effects of energy relaxation in the main peak and the vibronic side band. Representative SM2P traces are shown in Fig. 5(B) and (C) for an excitation wavelength of 610 nm and in Fig. 5(D) and (E) for a wavelength of 645 nm. To extract the energetic relaxation time constant, each trace was fit using a maximum likelihood estimation algorithm, which is more robust in the presence of noise as it includes a specific noise model. The observed Fisher information matrix was calculated and is directly related to the variance of our parameter estimation and asymptotically approaches the Cramér-Rao lower bound [32]. The standard error in the extracted time constants is determined through this variance and is generally less than 50 fs.
Fig. 5. (A) Absorption (solid) and fluorescence (dashed) spectra of Atto647N are shown with the chemical structure in inset. The laser pulses are overlaid ($\lambda _c$=610 nm, orange; $\lambda _c$=645 nm, red). Representative SM2P traces are shown for 610 nm excitation with values of 182$\pm$43 fs and 197$\pm$19 fs in (B) and (C), respectively, and for 645 nm excitation with values of 466$\pm$43 fs and 142$\pm$25 fs in (D) and (E), respectively.
3.1 Components of the energetic relaxation in Atto647N
SM2P traces on individual Atto647N were successfully performed 52 and 78 times for 610 nm and 645 nm excitation, respectively. To determine the distribution of energetic relaxation time constants, the extracted values were used to construct the histograms shown in Fig. 6. The histograms show a sharp peak and tail extended towards longer time constants, consistent with previous SM2P work [14,15]. The histograms were fit using a Gaussian mixture model in which two components were required to capture both the peak and the tail (Table 1). Gaussians were used as the simplest functional form that agreed with the measured distributions. The solution environment of Atto647N likely leads to multiple uncorrelated interactions between the dye and the surrounding molecules, which the central limit theorem predicts would lead to a Gaussian distribution. In environments where single interactions dominate, other distributions, such as an exponential Gaussian or a Gamma distribution, would be more appropriate and could better connect the skewed data to a physical phenomenon. We focus on the time constants extracted from the Gaussian mixture model, because the analysis was empirically found to more accurately and reproducibly extract the center values of the components as compared to the widths or standard deviations. The fit found a $\sim$115 fs time constant for the peak and $\sim$325 fs time constant for the tail. The ability of the 645 nm laser pulse to approximately measure the fast time component was confirmed using simulated data (Supplement 1, Fig. S2).
Fig. 6. Spectral independence of Atto647N energetic relaxation time constants. Histograms of energetic relaxation time constants were constructed for excitation at (A) 610 nm (N= 52) and (B) 645 nm (N=78). The histograms were fit (solid) with a two component Gaussian mixture model (dashed lines).
Table 1. Mean ($\mu$), standard deviation ($\sigma$), and amplitude ($A$) from a two-component Gaussian mixture model fit of the energetic relaxation time constants for Atto647N.
3.2 Interpretation of ultrafast time constants
We now consider the likely molecular origin of the two measured components. One-color SM2P spectroscopy measures the collective timescale of the dynamics through which the excited state moves out of resonance with the laser pulse. Previous ensemble ultrafast measurements extensively characterized the early timescale molecular dynamics, which can be divided into inertial solvation, diffusive solvation, and intramolecular vibrational relaxation (IVR) to non-optically coupled modes [31,33,34]. Inertial solvation is the fast timescale ($\sim$100 fs to 600 fs) response by individual solvent molecules to the new excited state and its dynamics. Diffusive solvation is the longer timescale ($\sim$ ps) collective reorganization of the solvent into a pseudo-equilibrium around the new excited-state electronic structure. While diffusive solvation occurs on timescales outside of the range of our experiment, inertial solvation contributes to the energetic relaxation time constants measured in SM2P. The final contribution is electronic dephasing due to the random fluctuations of the electronic transition energy known to occur in condensed phase systems [17,35,36]. Electronic dephasing occurs on a 50 to 100 fs timescale and can be modeled using the Bloch equations under pulsed excitation [17].
The histograms generated from the measured time constants include all of these contributions, which are well-described with two components (Fig. 6, Table 1). We assign the fast component ($\sim$ 100 fs) to contributions from electronic dephasing and the slower ($\sim$ 350 fs) component to a combination of inertial solvation and IVR. Previous experiments have shown an inertial-like response comes from coupled phonon modes in supercooled liquids [34], and similar effects may be present in the polymer matrix used here. Notably, the presence of two components in the single-molecule data suggests that each individual molecule is dominated by one of these components, potentially due to the composition of the neighboring polymer environment for each immobilized dye. The width of each component is narrow, with standard deviations consistent with the simulations of a single-value energetic relaxation time constant (Fig. 4), and thus is likely primarily due to Poissonian noise. The extracted standard deviations, therefore, suggest relatively homogeneous timescales, i.e., little molecule-to-molecule heterogeneity, in electronic dephasing, solvation, and IVR.
3.3 Spectral independence of energetic relaxation in Atto647N
To investigate the spectral dependence of energetic relaxation, SM2P measurements were performed for both the main peak (0-0 transition) and the vibronic shoulder (0-1 transition) with excitation at 645 nm and 610 nm, respectively. Histograms were constructed for both excitation conditions (Fig. 6(A) and (B)) and comparison of the distributions gives a p-value of 0.14, reflecting no statistically significant differences. Consistently, the values extracted from the Gaussian mixture model fit (Table 1) are similar. The lack of spectral dependence is comparable to ensemble ultrafast measurements on bodipy dyes as well as in theoretical models of solvation [31,33,34,37,38]. Although with the similarity in the random fluctuations that give rise to electronic dephasing, the contribution of IVR must also be spectrally independent. This suggests that relaxation pathways for the two excitation energies relies on a similar set of vibrational modes within the molecule or in the solvent.
4. Conclusion
In this work we developed a spectrally tunable version of SM2P, a technique that accesses the ultrafast dynamics of single emitters, and applied it to a widely-used fluorescent dye, Atto647N. These experiments revealed multi-timescale relaxation within the fluorophore with heterogeneity less than the Poissonian noise, suggesting the time constants of the early-time processes are insensitive to the local environment. While here we focused on spectral tunability, the quality of the SM2P data is also limited by the number of detected photons. In future versions of the experiment, the signal level could be improved through the addition of a second collection objective, incorporation of a cryostat for low temperature measurements, and/or detectors with improved quantum efficiency, such as those recently-developed using carbon nanotubes [39].
The versatility of our SM2P set-up allows for investigation into the distribution of energetic relaxation time constants for a multitude of optical systems. While the high fluences and multiple excitation cycles required for SM2P limit studies to systems that are photostable, there are multiple biological and material systems that meet this criterion, including fluorescent proteins, molecular aggregates, and quantum dots. For multi-choromophoric systems, processes such as exciton-exciton annihilation may lower the detected signal level [40], however, SM2P has been demonstrated on samples of this type. Indeed, the expanded spectral range will enable studies of photosynthetic proteins from many different species, such as the light-harvesting complexes from plants.
Funding
National Institute of General Medical Sciences (1DP2GM128200-01); Arnold and Mabel Beckman Foundation; Alfred P. Sloan Foundation; Canadian Institute for Advanced Research; Richard and Susan Smith Family Foundation.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are available from the authors upon request.
Supplemental document
See Supplement 1 for supporting content.
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