Nanoscopic Charge Fluctuations in a Gallium Phosphide Waveguide Measured by Single Molecules

We present efficient evanescent coupling of single organic molecules to a gallium phosphide (GaP) subwavelength waveguide (nanoguide) decorated with microelectrodes. By monitoring their Stark shifts, we reveal that the coupled molecules experience fluctuating electric fields. We analyze the spectral dynamics of different molecules over a large range of optical powers in the nanoguide to show that these fluctuations are light-induced and local. A simple model is developed to explain our observations based on the optical activation of charges at an estimated mean density of $2.5\times {10}^{22}{\mathrm{m}}^{-3}$ in the GaP nanostructure. Our work showcases the potential of organic molecules as nanoscopic sensors of the electric charge as well as the use of GaP nanostructures for integrated quantum photonics.

Figure 1

(a) An optical image of a nanoguide interfaced with two electrodes. The grating couplers on both sides of the nanoguide are covered by a polymer to shield them from irregularities in the $p\text{−}\mathrm{DCB}$ crystal [19]. The inset shows a scanning electron microscope image of a grating coupler before covering it with the polymer. (b) Simulated intensity profile of the TE mode in the nanoguide. (c) Extinction (blue) and fluorescence (red) spectra of hundreds of molecules. (d) Extinction and fluorescence spectra of one single molecule.

Figure 2

(a) Fluorescence signals of three molecules as a function of laser frequency detuning and applied external voltage. The dashed line points to broad instable resonances at high voltages. (b),(c) Temporal spectral dynamics of a single nanoguide-coupled molecule (M1) studied under two different applied dc voltages of 0 and 28 V. Individual spectra were recorded at the rate of 10 scans/s. The color scheme in (a)–(c) is chosen to highlight the molecular resonance frequency. (d),(e) Frequency fluctuations ${\sigma }_f$ (blue, diamond) and absolute tunability $\partial f/\partial V$ (orange, circle) as a function of applied voltage for two nanoguide-coupled molecules. The molecule in (d) was also M1. (f) Same as (d) and (e) but for a molecule far from the nanoguide. Black lines are linear fits to the absolute value of tunability.

Figure 3

(a) Autocorrelation function of the frequency trace of molecule M1 normalized to $C_{11}(0)$, measured at 10 V and an optical power of $3\times {10}^7\mathrm{photons}/\mathrm{s}$. Black line shows an exponential fit function, yielding an autocorrelation time of $\tau =1.0\mathrm{s}$. (b) Nanoguide transmission for repeated scans of the laser frequency. The blue symbols highlight the fitted resonance frequencies for each sweep. (c) Dependence of $\tau$ on the optical power ($P$) in the nanoguide. See SM for details on the power calibration [26]. Dots (diamonds) denote results obtained through extinction (fluorescence) measurements. The color coding indicates the sweep rate used to record the frequency traces. The straight line shows a fit to $\tau \propto P^{-1}$. (d) Magnitude of the center frequency fluctuations.

Figure 4

(a) Sketch of the arrangement of molecules labeled M1, M2, and M3 along the nanoguide. (b) Examples of transmission spectra obtained simultaneously at two frequency intervals separated by about 50 GHz. Colored lines indicate the evolution of the resonance frequencies. (c) Cross-correlation functions of M1–M2 ($C_{12}$, magenta) and M2–M3 ($C_{23}$, mustard). (d) Frequency fluctuation rate $1/\tau$ (blue) as a function of the displacement of an auxiliary focused laser beam along the nanoguide over a molecule; see (e). The rate is normalized to that in the absence of the auxiliary excitation. The red curve shows the intensity profile of the excitation laser’s focus spot mapped by the fluorescence of the molecule. (e) Sketch of the arrangement when a second laser beam is shone in the direction normal to the plane of the chip and its focus spot is scanned along the nanoguide.

Figure 5

Upper plots: Histograms of the step-size distributions for the experimental data (a) and three synthetic datasets at different densities $n_q$ (b)–(d). Gray curves denote fits to a Gaussian distribution. Lower plots: Ratio of the occurrences to their corresponding Gaussian functions after an offset correction (see SM [26]). (e) The symbols show the dependence of the non-Gaussianity parameter $\eta$ (see text) on the simulated charge density used. The blue horizontal line corresponds to the experimental data, and the black line signifies the baseline of our analysis caused by fit errors [26].