Observation of bound and antibound states of cavity polariton pairs in a CuCl microcavity

We observed the antibound state, as well as the bound state, for cavity polariton pairs in a planar CuCl microcavity by spectrally resolved four-wave mixing. We obtained dispersion curves of the bound and antibound states by changing the incident angle of the pump pulses corresponding to the cavity detuning. The dispersion curve for the bound state suggests that the bound state is mainly composed of a bare biexciton and is weakly coupled to the cavity photons. The dephasing time of the bound state was faster than that of a bare biexciton in a thin sample, supporting the hypothesis that the bound state is coupled to the cavity photons. On the other hand, the antibound state consists of two lower polaritons having the same spin. The clear observation of the antibound state can be qualitatively explained by the phase-space filling, which reduces the Rabi splitting.

Figure 1

Dip positions in the reflection spectra of the CuCl microcavity as a function of the incident angle. Red lines are fitting curves using a 3$\times$3 phenomenological Hamiltonian with parameters $\hslash g_3=20$ meV, $\hslash g_{1,2}=33$ meV, $\Delta =-88$ meV. Dashed lines are the dispersion curves of the $Z_{1,2}$ and $Z_3$ excitons and the cavity photon mode. Inset: Angle-resolved reflection spectra of the CuCl microcavity obtained at 10 K. LPB, MPB, and UPB represent the lower, middle, and upper polariton branches, respectively.

Figure 2

(a) Schematic view of the FWM experiment. (b) The polarization selection rule of a five-level system. $|g\rangle$ represents the ground state. $|J=0\rangle$ and $|J=2\rangle$ are the bound and antibound states for the polariton pairs, respectively. $|LP;\pm 1\rangle$ are the lower polariton states having orbital angular momentums of $\pm 1$.

Figure 3

FWM spectra observed at $\tau =-200$, 0, and +200 fs for the (a) cocircular pump, (b) cross-linear pump, and (c) parallel-linear pump polarizations. (d) The excitation density ($I$) dependence of the peak intensity of the FWM spectrum at $\tau =0$ fs under the cocircular pump polarization. The excitation densities of the first and second pulses were the same: $I=I_1=I_2$.

Figure 4

Incident-angle dependence of the FWM spectrum at (a) $\tau =-200$ fs and (b) $\tau =200$ fs under the parallel-linear pump polarization.

Figure 5

(a) Peak positions of the lower polariton, bound, and antibound states observed in the FWM spectra plotted as functions of the incident angle of the pump. Also plotted are the fitting curve for the dispersion curve of the lower polariton obtained from Fig. 1 and the energy difference, $E_{\text{BX}\to \text{LP}}=E_{\text{BX}}-E_{\text{LP}}$, between the biexciton in a bulk crystal, $E_{\text{BX}}$, and the lower polariton, $E_{\text{LP}}$. (b) Dependences of the bound-state energy, $E_{\text{BS}}$, and the antibound-state energy, $E_{\text{AS}}$, on the incident angle, together with $E_{\text{BX}}$ and $2E_{\text{LP}}$.

Figure 6

FWM responses monitored at the signal peak positions of the bound state and antibound state in the microcavity for $\theta ={31}^{\circ }$, together with the biexciton in the 50-nm-thick CuCl film.