Quantum electrodynamics at room temperature coupling a single vibrating molecule with a plasmonic nanocavity

Interactions between a single emitter and cavity provide the archetypical system for fundamental quantum electrodynamics. Here we show that a single molecule of Atto647 aligned using DNA origami interacts coherently with a sub-wavelength plasmonic nanocavity, approaching the cooperative regime even at room temperature. Power-dependent pulsed excitation reveals Rabi oscillations, arising from the coupling of the oscillating electric field between the ground and excited states. The observed single-molecule fluorescent emission is split into two modes resulting from anti-crossing with the plasmonic mode, indicating the molecule is strongly coupled to the cavity. The second-order correlation function of the photon emission statistics is found to be pump wavelength dependent, varying from g(2)(0) = 0.4 to 1.45, highlighting the influence of vibrational relaxation on the Jaynes-Cummings ladder. Our results show that cavity quantum electrodynamic effects can be observed in molecular systems at ambient conditions, opening significant potential for device applications.

In Fig. 1b, we show the darkfield spectra evidence a consistent red-shift of 20 nm when a single Atto647 dye molecule is embedded inside the cavity. In both cases the same DNAo, same NPs, and same conditions are used. We comment here on the possible reasons for this observation. We start by calculating the coupled plasmon mode area which is given by = / 2 (see Ref. [3]), where is the nanoparticle diameter, is the gap size, and = 2.1 is the measured refractive index of DNAo in these structures (see [1], and comment below) so we obtain = 36 nm 2 . Using an effective area for each dye molecule of ≈ 1 nm 2 and the on-resonant refractive index of a single dye molecule as ≈ 4 (see Ref.4), the effective refractive index in the gap can be estimated as The estimated corresponds to an increase in effective gap refractive index of Δ = 5%. Using a simple 2D Fabry-Perot resonator model for the coupled plasmon resonance, based on nanoparticle facet width we get discrete wavelengths supported by the gap 5,6 where 1 is the first zero of the Bessel function, and is the plasma wavelength for Au ~148nm with background permittivity ∞ . The fractional change in wavelength is then From Eq. (S3), we obtain a fractional change in wavelength of ~2%, which is close to the observed 3% wavelength redshift. Therefore, the observed shift in the cavity resonance is indeed plausibly due to the change in effective refractive index of the gap. Such shifts are also expected from the approach of strong-coupling in the regime utilised here, since exactly the change in round trip phase in the nanocavity is responsible for strong coupling and shifts the coupled mode plasmon.
We note the refractive index of the DNA origami comes from previous papers [37,39,41] which extract it from careful fitting of coupled mode wavelengths (ie. in close proximity to Au surfaces). Additional contributions from other effects such as facet size, uncertainty in gap size, and screening effects due to free electrons in NP, are beyond the scope of this paper. The Rabi oscillations are described using the probability that an electron is left in the excited state | ( )| 2 and is given as 7,8 , is the time, is the damping rate, Rabi frequency Ω R = | 12 0 /ℏ|, 12 is the transition dipole moment, 0 is the electric field amplitude, and ℏ is Planck's constant. The pulse area Θ is then calculated using 8 where is the pulse duration.
We note that these oscillations are frequently lost on the second experimental run on the same NPoM (as shown in Supplementary Figure 2) because the plasmon cavity mode is shifting from the movement of Au atoms (see [49,50]). Although some emission is still seen, it is no longer in resonance, as clearly observed in Fig.3a. The molecule is surprisingly robust even at higher excitation powers (see Supplementary Figure 3), since there is no observable step-wise decrease in intensity, which would be obtained from bleaching. A slower decrease in intensity is observed which is a result of the red-shift of the cavity resonance that is detuned from the molecule emission peak and the excitation overlap with the pump wavelength.

Supplementary Note 6: Second-order intensity correction ( ): measurement and simulation
CW excitation cannot be used for the 2 measurements as it would show a deep dip with only a sub-100fs recovery time. Since single-photon detection averages >0.3ns, then this dip would be electronically smoothed out by 0.3ns/100fs~3000 times, making the dip now 3000x broader and 3000x smaller and impossible to see over the typical noise. Instead pulsed excitation has to be used, with spacings in time larger than this instrumental time resolution. The 100fs excitation needs to match the emission time (which is <1ps from the Purcell enhancements measured) to avoid reexcitation of the dye within a single pulse.

Measurements at 610 nm:
As described in the main manuscript, we performed correction measurements at two different excitation wavelengths: 520 nm and 590 nm. We also performed the measurement at 610 nm with an input power ~2 . We detect light from 650 nm to longer wavelengths. The result shown in Supplementary Figure 7 reveals that the detected count is over one order of magnitude higher for 610 nm pump than at the other two excitation wavelengths. The reason for this higher signal is because the excitation wavelength is closer to the absorption peak, which is at 645 nm (see Fig. 1c in the main manuscript), therefore the emitted intensity increases and the SERS signal collected also increases. As a result of a high contribution by the SERS signal, the 2 (0) quickly tends to 1 (Supplementary Figure 7b), which is expected for an uncorrelated light source. Figure 7:(a,c) Second-order intensity correlation (a) with the dye present at 610 nm excitation wavelength, and (c) without the dye at 590 nm excitation. (b,d) Evolution of 2 (0) vs measurement time corresponding to (a,c). Black dashed line shows time at which the upper panels are taken.

Simulation of detection efficiency on background emission:
In order to estimate the influence of the extra uncorrelated SERS-enhanced metallic emission on the estimates of 2 (0), we perform numerical simulations of photon statistics to generate arrival times of photons and their correlations. Arrival times of uncorrelated photons are generated using a Poissonian distribution with a mean ~1. For single photons (sub-Poissonian light), we use the binomial distribution to generate the arrival times. Bunched photons (e.g. thermal or chaotic light) can be described by a super-Poissonian distribution that has a variance greater than the mean. An example of such is Bose-Einstein distribution, which only applies to a single mode of a radiation field and tends to the Poissonian distribution at large numbers of modes 8 . For each of the three photon statistics regimes here, we randomly draw 100 photons from the respective distributions and simulate the procedures of the start-stop experiment: The stream of randomly generated photons is equally split into two and the time delay between the two streams of photons are computed. In our simulation of start-stop experiments, arrival times with more than two photons are counted as one photon only ignoring the rest because of the dead-time of the detectors. We obtained 2 (0) from the histogram of the time delays, as explained in the main manuscript and then repeat this procedure 5000 times. We vary the fraction of uncorrelated photons , such that when = 0, the generated photon distribution is entirely the correlated photon component and for = 1, the generated photons are entirely uncorrelated, giving 2 (0) = 1. For 0 < < 1, the number of uncorrelated photons are 100 and the rest are correlated photons, therefore the total number of photons is constant. In addition, at = 0, we used different initial values of 2 (0) by changing the mean (from 0.3 to 1) of the Bose-Einstein distribution for bunched photons. For anti-bunched photons, we introduced a fraction of uncorrelated photons to the correlated photons at = 0 as this would be the case from multiple excitations within a pulse, so that 2 (0) > 0 at = 0.
In Supplementary Figure 8(a,b) we show the results of these simulations. In the green curve of Supplementary Figure 7(a), 2 (0) increases from zero (an ideal photon source) to one as the contribution of the uncorrelated photons increases. When 2 (0) ≠ 0 at = 0, 2 (0) approaches one at different rates depending on the initial value of 2 (0).