## 4 Experimental Study
### Results  
First, we investigate the fluorescence response of the perovskite outside the cavity. Figure 6 shows the fluorescence response of the perovskite probes in solution. The excitation wavelength used for fluorescence measurement was 440 nm. The observed emission spectrum is relatively narrow (for organic and metalorganic compounds), with the maximum around 530 nm and full width half maximum (FWHM) approximately 25 nm. Figure 5: Structure of CsPbCl\({}_{3}\) perovskite is based on crystal structure from ICSD database 201250 [21]. In order to understand better the radiative response, we performed time-resolved measurements of the emitted fluorescence intensity (Figure 6b). The best fits of experimental results are obtained with a double exponential function that gave rise to a long decay time (of ca. 12.2 ns) that is related to the actual lifetime of the probe in this particular environment, and a short decay time (of ca. 1.6 ns), is associated with different nonradiative processes that affect the radiative dynamics of the dye. After that, we perform the steady-state investigation of the perovskite embedded into the plasmonic cavity at two different temperatures (room temperature 298 K and 10K). The sample was excited from outside the cavity; the excess energy \(\delta\omega\) is necessary for creating a complex metastable excited state that will firstly follow a complicated non-radiative decay process before arriving at the radiative excited dipole state \(|e,0_{c}\rangle\) considered in Section 3. The steady-state response of the perovskite within the cavity is presented in Figure 7 and shows the signature of Rabi splitting that confirms that strong coupling between cavity and probe is achieved. As can be seen from Figure 7b, the splitting remains observable at room temperature, even though the height of the peaks diminished by then due to various sources of decoherence that increase with increasing temperature of the sample. Figure 7a exhibits the typical response of a Fabry-Perot cavity. Figure 6: (**a**) Fluorescence steady state spectrum of perovskite in solution; (**b**) Fluorescence decay time response of the perovskite in solution fitted with a double exponential function. Figure 7: (**a**) Optical response of the cavity with emission spectrum from perovskite fluorophores in solution (inset); (**b**) emission spectrum from perovskite fluorophores in cavity—signature of Rabi splitting. After a steady-state fluorescence study that shows the signature of the strong-coupling through Rabi splitting, the fluorescence time-resolved study reveals the effect of the strong coupling on the dynamics of the excited state. The theoretical decay time of the cavity is comparable, in the strong-coupling regime, to the survival time of the excited state \(\ket{e,0_{c}}\). It can be estimated by measuring the width of one of the Lorentzian peaks of Figure 7. By so doing, we estimate the lifetime of the cavity to be in the picosecond range. The distance between the two peaks makes it possible to estimate the value of the coupling constant \(g\) from which the ratio \(g/\gamma_{c}\) is thus predicted to be equal to 5.9, which confirms once more that we are well in the strong-coupling regime. Results of the measurement show that, as in the case of the probe in solution, the perovskite radiation dynamics within the cavity are best fitted with the double exponential functions. Like the energy splitting, the two decay signatures survive at room temperature (as can be seen from Figure 8. At room temperature (298 K), the perovskite within the cavity gave rise to a long decay time (of ca. 7.7 ns) that is related to the actual lifetime of the probe within the cavity and a short decay time (of ca. 0.87 ns) that is associated with different nonradiative processes that affect the radiative dynamics of the dye. The probe's lifetime within the cavity is significantly shorter (37%) compared to the lifetime in solution (decay rate increases).