- Chinese Optics Letters
- Vol. 20, Issue 7, 073602 (2022)
Abstract
1. Introduction
Organic molecules are attractive to both physicists and chemists because molecules could have high quantum efficiencies in light emission and be chemically synthesized to have transitions at desired wavelengths. In the past several decades, single molecules embedded in solids, as isolated individual quantum systems, have become an attractive class of sources of single photons since a single two-level system cannot emit two photons simultaneously, as each excitation and emission cycle requires a finite time[
The quantum efficiency of an emitter indicates the ability to emit a photon once an excitation photon is absorbed and is defined as , where and are the radiative decay rate and nonradiative decay rate of the emitter, respectively. While the theoretical definition of quantum efficiency is crystal clear, its experimental measurement is highly nontrivial. In the past two decades, there have been several experiments reporting the measurements of absolute quantum efficiency of single emitters[
In this work, we present a simple method to experimentally probe fluorescence quantum efficiency of single DBT molecules embedded in AC microcrystal by monitoring the fluorescence lifetime change during the process of natural sublimation. The decrease of the thickness of the microcrystal due to sublimation induces the change of the optical environment of the molecules and, consequently, the change of the Purcell factor or the local density of optical states (LDOS), which manifests through the modification of the fluorescence lifetime[
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2. Experiments
DBT-doped AC (DBT:AC) microcrystals with preset concentrations are prepared through a co-sublimation process[
Figure 1.(a) Sketch of the experimental setup (see text for details). (b) Fluorescence image of single dibenzoterrylene (DBT) molecules embedded in an anthracene (AC) microcrystal obtained through confocal scanning; (c) photoluminescence (PL) time trace and (d) normalized second-order photon correlation function of fluorescence from a DBT molecule. The inset in (d) is the emission spectrum of the same molecule. (e) Atomic force microscope (AFM) topographic image of a part of an AC microcrystal. (f) Left: schematic illustration of the sublimation process of the AC microcrystal; right: cross-sectional plots of the height along the same blue dashed line shown in (e) at different times, which demonstrate the sublimation process.
3. Results
Figure 1(b) shows a confocal-scanning fluorescence image of single DBT molecules embedded in an AC microcrystal in a small region under CW laser excitation at a wavelength of 730 nm. Each molecule is spatially well separated and indicates a proper concentration of molecules in the sample. Figures 1(c) and 1(d) present a recorded PL time trace and normalized second-order photon correlation function from the same molecule. The nonblinking fluorescence has a count rate of about 190 kcps (cps, counts per second) with a background rate of 1 kcps. The curve exhibits a pronounced antibunching dip of at zero time delay. The inset of Fig. 1(d) is the emission spectrum of the molecule. These results confirm that the individual DBT molecule inside the AC microcrystal has stable and pure single-photon emission. The crystalline DBT:AC microcrystal has flat surface, which is shown via an AFM topography image in Fig. 1(e). As sketched in Fig. 1(f), when the microcrystal is exposed in the air, sublimation brings decreasing thickness of the AC crystal, which is indicated by cross-sectional plots of the height along the blue dashed line in Fig. 1(e).
The structure of the sample we measured is depicted in Fig. 2(a), where represents the thickness of the AC microcrystal, and is the height of the molecule above the glass coverslip. As illustrated in Fig. 2(a), the emission dipole moment of the DBT molecule is aligned with the axis of the crystal[
Figure 2.(a) Schematic diagram of the sample structure. (b) Measured and simulated back-focal plane (BFP) images of the emission from a single molecule oriented along the b axis of the AC microcrystal. (c)–(f) Measured and fitted PL decay curves from the same DBT molecule at different times. Insets: AFM topographic images of the region of the AC microcrystal where the molecule is located. The red star marks the location of the measured molecule. Scale bar: 500 nm.
Two different DBT molecules, molecule #1 and another labeled as molecule #2, are then studied in comparison. The crystal thickness-dependent total decay rates () of the molecules are obtained from the measured lifetimes () and shown in Fig. 3(a). The total decay rate can be expressed with , as contributed by the radiative and nonradiative decay rates. We observed that the two molecules still survived and were producing stable fluorescence emission even 4 h after the AFM scans and lifetime measurements were finished. At that time, the crystal thickness should have been further reduced by tens of nanometers due to sublimation. Therefore, the target molecules must be buried deep down below the top surface of the crystal, and the nonradiative decay rates can be regarded as constant during the sublimation. So, the decrease of the total decay rates stems from the change in the radiative decay rates related to the LDOS. We describe the LDOS with the Purcell factor , which is by definition and can be numerically determined as the ratio between radiated powers of a classical dipole (Chap. 8 of Ref. [33]), i.e.,
Figure 3.(a) Measured and fitted total decay rates (1/τ) of two different DBT molecules as functions of the AC microcrystal thicknesses. (b) Purcell factor distribution versus emitter dipole position h and the microcrystal thickness H.
Here, is the radiative decay rate of a DBT molecule in unbounded AC crystal. and are, respectively, the radiated powers of a classical dipole mimicking the DBT molecule in the AC microcrystal and unbounded AC crystal environment. Then, we calculated the two powers in the frequency domain with finite-element method based COMSOL Multiphysics. The computational domain containing the dipole and dielectric environment is truncated with perfectly matched layers to absorb outgoing waves and discretized with nonuniform tetrahedral meshes optimized to guarantee convergence. The dipole is aligned to the axis and working at the wavelength of 781 nm. The anisotropy of the AC crystal has been taken into account in the simulation as , , [
During the sublimation, the position of a specific molecule remains unchanged. Thus, the measured lifetime is only a function of . Using the intrinsic quantum efficiency defined by , we can rewrite Eq. (2) as
Equation (3) provides a model to explain the sublimation-induced lifetime change. The unknown parameters , , and can be further extracted by fitting the model to the measured lifetimes at different crystal thicknesses. When we stopped the lifetime measurements, the crystal still had a thickness of 120 nm. Considering that the measured molecules are buried deep down below the top surface, the emitter position should be fitted in a range from 0 nm to 90 nm, which is consistent with the range of the map in Fig. 3(b). According to the simulated , we find the best fitted set of , , and , which minimizes the residual error between theoretical calculation based on Eq. (3) and measured lifetime data. The fitted results are plotted in Fig. 3(a). For molecule #1, we find , , and ; for molecule #2, , , and . The average intrinsic quantum efficiency of 95% agrees with the reported near-unity values for DBT molecules at the ensemble level at low temperature[
4. Discussion
We utilized the natural sublimation of the AC microcrystal, which induces optical environment change for embedded DBT molecules and experimentally probed fluorescence quantum efficiency of single DBT molecules by monitoring the fluorescence lifetime change due to the optical environment variation. By identifying the orientation of the molecule emission dipole from the radiation pattern through BFP imaging, we established a Purcell factor distribution as a function of crystal thickness and molecule position to describe the sublimation-induced lifetime change and analyze the quantum efficiency. Based on a series of measured AC crystal thicknesses and lifetimes recorded on the same molecules, we deduced the near-unity intrinsic quantum efficiency of the DBT molecule in the AC microcrystal.
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