Realizing room-temperature strong coupling of single-exciton with plasmons by controlling quantum exceptional point

Single-exciton strong coupling with plasmons is highly desirable for exploiting room-temperature quantum devices and applications. However, the large plasmon decay makes the realization of such strong coupling extremely difficult. To overcome this challenge, here we propose an effective approach to easily achieve the single-exciton strong coupling at room temperature by controlling quantum exceptional point (QEP) of the coupling system via matching the decay between the localized plasmon mode (LPM) and exciton. The good match can be reached by suppressing the LPM’s decay with the use of a leaky Fabry-Perot cavity. Experimental results show that the LPM’s decay linewidth is greatly compressed from ~ 45 nm to ~ 15 nm, which is close to the excitonic linewidth (~ 10 nm), pushing their interaction from the Fano interference into the strong coupling. Our work opens a new way to flexibly control the QEP and more easily realize the single-exciton strong coupling in ambient conditions.


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interaction distance provides advantages to realize strong coupling at the single-QE level.
Experimentally, the dark-field scattering measurements of individual Au@Ag NR/J-aggregates hybrids on the indium tin oxide (ITO)-coated glass substrate are firstly performed. Figure 1a shows the scattering spectra of the bare cuboid Au@Ag NR with the size of 65´36 nm, which is on resonance with the exciton absorption. The measured scattering spectrum from the hybrid system consisting of an Au@Ag NR covered around with single-layer J-aggregates is plotted by the solid pink curve with an evident spectral splitting of ~ 69 meV (Fig. 1b). The theoretical scattering spectrum is displayed by the dotted black curve, which is obtained by the following Eq. with Eq. (3), N is the only fitting parameter to be determined.
In order to further validate the above-mentioned conclusions, we exam the dispersion of spectral splitting with different detunings for individual Au@Ag NR/J-aggregate hybrids with different NR size. The normalized scattering spectra of individual Au@Ag NR/J-aggregate hybrids with different detunings are displayed in Fig. 1c, in which a vague anticrossing behavior with ~ 69 meV can be observed. The scattering spectra of three typical single Au@Ag NR/Jaggregate hybrids with different detunings can be found in Supplementary Fig. 7. Figure 1d gives the theoretical dispersion on the detuning ( ) obtained by Eq. (3) (Fig. 1f). despite of the fact that the spectral splitting is evident. This interesting phenomenon has been detailedly discussed in our recent theory work and the corresponding interaction is assigned to the pseudo-strong coupling regime 37 , in which the spectral splitting arises from the Fano resonance 22,29,38 . This result also gives an experimental proof to the prediction made in ref. 37 that the equality assumption of spectral splitting and level splitting is invalid in usual plasmon-exciton coupling systems with large dissipative decays and remarkable decay mismatch between the two coupling subsystems. In the following text, we will theoretically and experimentally demonstrate how the proposed approach, that lowers the critical coupling-strength at the QEP by suppressing the LPM's decay to match with the exciton's decay , and pushes the interaction of the single exciton and LPM from the Fano resonance into strong coupling.  schematic diagram of such a plasmonic-photonic hybrid system by loading a single Au NR on the surface of a leaky FP cavity constructed by three dielectric layers of Si/SiO2/Si3N4. The dashed gray curve in Fig. 2b gives some typical FP-cavity modes in the spectral region of 550-775 nm.

Figure 1 | LPM-exciton couplings in single
The EFs of the FP-cavity modes can be leaked into the free space and formed an EM environment When the synergistic interaction between the NR and the FP-cavity mode TM2 is on resonance, interestingly, the EF intensity on the surface of the NR can be improved compared to the two separate entities without synergistic interactions (Fig. 2d). Figure 2e shows that the total EF (|E| 2 ) on the surface of the FP-cavity-engineered NR, which has been enhanced by ~3 times compared to the NR located on the bulk Si3N4 substrate. The merits of the lowered dissipative decays 48,49 and the enhanced plasmonic EFs make the cavity-engineered NRs an ideal platform for implementing the quantum manipulation of light-matter interactions at room temperature. Next, we experimentally demonstrate the suppression of the dissipative decay for the Au@Ag NRs by applying this general strategy. On the other hand, for a given FP-cavity mode (for instance, TM1'), after the LPMs of different cuboid NRs sculpted by this mode, the new formed ELPMs have almost same resonance frequencies and decay linewidths with small deviations (Supplementary Fig. 11). This deviation can also be tuned in a broad spectral region by FP cavities with different cavity length ( Supplementary Fig. 12). These resonance frequency  Fig. 3e (ii)), the decay linewidths of the ELPMs are remarkably narrowed.   Fig. 4b. It should be mentioned that the aspect ratios of the two different cuboid Au@Ag NRs (Fig. 4a, b) are almost the same, which lead to almost the same resonance wavelengths and decay linewidths (Fig. 3e) when they are locating in the same dielectric environment (Supplementary Table 2). From Fig. 4a, one can see that the experimental and the theoretical results are in a good accordance again. compared to that ( = 30.75 meV) of single-exciton coupling with the Au@Ag NR without cavity-engineered (Fig. 4c), in this case, a dramatically lowered = 4.5 meV at the QEP was achieved (Fig. 4d) Typical dark-field scattering spectra of the single-exciton-coupled NRs with different detuning localized on this leaky FP cavity are presented in Supplementary Fig. 13. More scattering spectra of the single-exciton-coupled NRs ordered according to the detuning shown in Fig. 4e Table. 3). These results clearly indicate that we have successfully achieved the single-exciton strong coupling at room temperature in single FP-cavity-engineered Au@Ag NRs.  (3) with = 1, ~55 meV ( Supplementary Fig. 8b), ~36 meV and ~28.8 meV. f Quantum steps for the effective coupling coefficient, , observed as one, two and three-exciton coupling cases for the hybrid NRs isolated from the sample treated with the 1.0-μΜ dye solution.
The scale bar in the insets of (a) and (b) is 50 nm.

Discussion
The control of of the coupling systems also has significant influences on the quantum coherence properties in the plasmon-exciton coupling systems. As is well known that when the interaction is in the strong coupling regime, plasmon and exciton will give up their separate identities and the hybrid quasiparticles of plexciton can be formed, which is also a reflection of the quantum coherence between these two components. Figure 5a shows the plasmonic and exciton can also be obtained from the strong coupling case in Fig. 4a, which is more than two times larger than that (~0.83) of the weak coupling case shown in Fig. 1b. To the best of our knowledge, this cooperativity is the maximum for single-exciton strong coupling with plasmon modes at room temperature 4,26-29 . In Fig. 5b, we list the statistics of for the single-exciton strong coupling with different NRs. An average cooperativity ~ 2.04 is observed, which is much larger than those  Cooperativities of the individual single-exciton-coupled NRs located on the FP cavity (red stars) and the ITO substrate (green triangles), which are calculated from the experimental data in Fig. 1c and Fig. 4e, respectively.
In summary, we have revealed that the high critical coupling energy at the QEP due to large mismatch between the dissipative decays of the QE and LPM seriously hinders the realization of the single-QE strong coupling at room temperature. It is theoretically and experimentally demonstrated that the good decay match between the two coupling subsystems can be achieved by suppressing the dissipative decay of the LPM with use of a leaky Fabry-Perot cavity, resulting in a considerable decrease of the critical coupling-energy at the QEP. The proposed strategy gets rid of the extreme conditions (such as cryogenic temperatures and ultrahigh vacuum, or ultrasmall QEP g 19 mode volume) previously required by the single-QE strong coupling with photonic modes, which makes its realization at room temperature much easier. Our work not only opens a new path to easily realize the room-temperature single-QE strong coupling with photonic modes, but also provides a flexible way to control and access the QEP in ambient conditions. The leaky Fabry-Perot (FP) cavities constructed by three dielectric layers of Si/SiO2/Si3N4 were fabricated using the method of inductively coupled plasma chemical vapor deposition (ICPCVD, PlasmaPro System100

Methods
ICP180-CVD，Oxford，UK). The schematic of the fabrication process can be found in Supplementary Fig. 16.
Specifically, 3000-nm thick stoichiometric SiO2 on the single crystal silicon substrate was firstly deposited, next, a 200-nanometer film of silicon nitride (Si3N4) was deposited in the same way. After these two simple processes, 21 the FP cavity sample was constructed. After the measurement using the thin-film analyzer (Filmetrics, F20-UV/F20-UVX/F20/F20-EX, USA) , we found that the final thickness of SiO2 (Si3N4) was ~3008 nm (~217 nm), and the surface of the silicon nitride structure was found to be rather flat and smooth. It is worth pointing out that the sandwich Si3N4/SiO2/Si slab cavity structure developed here is particularly robust. Unlike typical plasmonic cavities which surface or shell is oxidized with time, almost no performance degradation is observed even up to one year. After the FP cavity fabricated, individual Au@Ag NR/J-aggregate hybrids were dropped on the up surface of the cavity for next dark-filed scattering measurements.
Optical and morphology characterization. Extinction spectra were measured on an ultraviolet-visible-nearinfrared spectrometer (Lambda 950, PerkinElmer) with a high spectral resolution of 0.08 nm. The TEM images were taken by a 2010HT TEM machine (JEOL Inc., Japan) operated at 100 kV. The high-resolution TEM images were obtained by Titan G2 60-300 (FEI Inc., America) microscope operated at 300 kV. The SEM images were taken by Auriga-39-34 (Zeiss Inc., Germany) microscope operating at 5.0 kV.
Dark-filed scattering measurements. The schematic of our dark-filed scattering measurements can be referred in ref. 28 . Before the scattering measurements, 25 μL of the Au@Ag NR/J-aggregates bulk solution was dropcasted onto the up surface of the FP cavity (or the ITO coated glass substrate). After about one min, the droplet was removed, and the samples were washed with deionized water and dried under nitrogen conditions. Then, the individual Au@Ag NR/J-aggregate hybrids isolated from the sample could be formed and fixed on the surface of FP cavity (or the ITO-coated glass substrate). Note that, the ITO material has a reflex index very close to the Si3N4 in the visible spectral range, but has a much better electrical conductivity which allows the Au@Ag NRs to be well characterized with both SEM and dark-field imaging). In order to obtain the scattering spectroscopy of the individual hybrids, we combined dark-filed microscopy with SEM of the same field of view to correlate elastic scattering spectra and structures on the level of single hybrid NR. The scattering images and spectra of the individual Au@Ag NR/J-aggregate hybrids were recorded on a dark-field optical microscope (Olympus BX51, Olympus Inc.) that was integrated with a monochromator (Acton Spectra Pro 2360, Acton Inc.), a quartz tungsten halogen lamp (100 W), and a charge-coupled device camera (Princeton Instruments Pixis 400BR_eXcelon). To obtain clean scattering signals from a single isolated hybrid NR, the commercial 22 spectrograph equipped with an entrance slit was set at ~100 nm and the camera was cooled to -70℃ during the measurements.
For collection of the scattering spectra of the individual hybrids, the light was launched from a dark-field objective (100×, numerical aperture 0.80), and the light scattered in the backward direction was collected by the same objective. The color scattering images were captured using a color digital camera (ARTCAM-300MI-C, ACH Technology Inc.) mounted on the imaging plane of the microscope.

Data availability
The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.