Vacuum Rabi splitting in a plasmonic cavity at the single quantum emitter limit

The strong interaction of individual quantum emitters with resonant cavities is of fundamental interest for understanding light–matter interactions. Plasmonic cavities hold the promise of attaining the strong coupling regime even under ambient conditions and within subdiffraction volumes. Recent experiments revealed strong coupling between individual plasmonic structures and multiple organic molecules; however, strong coupling at the limit of a single quantum emitter has not been reported so far. Here we demonstrate vacuum Rabi splitting, a manifestation of strong coupling, using silver bowtie plasmonic cavities loaded with semiconductor quantum dots (QDs). A transparency dip is observed in the scattering spectra of individual bowties with one to a few QDs, which are directly counted in their gaps. A coupling rate as high as 120 meV is registered even with a single QD, placing the bowtie-QD constructs close to the strong coupling regime. These observations are verified by polarization-dependent experiments and validated by electromagnetic calculations.

the main text are shown, with four QDs (left) and two QDs (right). Rabi splitting is observed even with unpolarized light (top row), but is strongest when the laser polarization is parallel to the bowtie long axis (0, middle row). The splitting vanishes when the polarization is rotated by 90 (bottom row).

Supplementary Figure 7
Electromagnetic simulations of coupling. a. The distribution of the coupling rate (in eV) of a quantum emitter with an oscillator strength of 0.6 near a single prism. The white bar represents 10 nm. b. Distribution of the coupling rate as a function of distance from one of the prisms of a bowtie (red) or from a single prism (green), along the center line and starting at the position where the edge of an 8 nm QD is 0.5 nm away from the prism.

Supplementary Figure 8
Schematic of the dark-field microspectromter. The setup was based on an inverted microscope equipped with a dark field condenser (NA=0.9), a 75 W Xenon lamp (Olympus) and a 100× oil immersion objective (NA=0.6). A combination of a light-stop with the toplens of the condenser was used to exclude the light propagating along the normal to the sample plane, such that the light rays impinged on the sample at an angle of 70 degrees. A SpectraPro-150 spectrograph with a 1200 g/mm grating (Acton) and a Newton spectroscopy CCD camera (Andor Technology) were used to disperse the scattered light and register spectra. Polarization of the excitation light was controlled by a polarizer and an additional light-stop that passed the light only through a narrow selecting sector. When the sector was aligned such that the axis of the polarizer was normal to the bisecting line of the sector, the light at the sample was predominantly s-polarized.

Supplementary Note
The absorption spectrum of a semiconductor QD (Supplementary Figure 2) does not have a simple line shape like the emission spectrum, due to the absorption into higher energy states.
How does that affect the coupling process? A good way to think about this problem is to envision this process in the time domain. First, a photon is injected into the cavity. As this photon bounces in the cavity it interacts with the quantum emitter. If the photon energy is in resonance with the emitter it absorbs the photon. Indeed, a QD contains more than a single exciton state. Each of the states that overlap the photon energy can absorb the photon. This photon has to be re-emitted. Typically a fast relaxation then brings the QD to the lowestenergy exciton, so the emission is from that exciton. However, irrespective of which exciton emits, unless the emission spectrum overlaps strongly with the cavity spectrum the photon will escape the cavity. If there is such overlap the photon stays in the cavity, and the process can be repeated more than one time, which is the essence of strong coupling.
The bottom line is that a prerequisite for strong coupling is good overlap between both the absorption and emission of the QD and the cavity. Whether one exciton state is involved or more should not matter, just as in the case of molecules the number of vibronic states involved does not seem to matter (a discussion of this issue for molecules is given in the review of Torma and Barnes, reference 9 of the manuscript, section 4.2). This issue might be approached through a detailed quantum calculation.