Observation of diffusive and dispersive profiles of the nonequilibrium polariton-condensate dispersion relation in a CuBr microcavity

We have investigated the dispersion relation of polariton condensates in a CuBr microcavity with the use of angle-resolved photoluminescence (PL) spectroscopy at 77 K. The polariton condensation was clearly confirmed by the thresholdlike changes in the PL intensity, energy, and bandwidth of the lower polariton at a zero in-plane wave-vector $k_{\parallel }=0$ as a function of excitation power density. A blueshifted flat dispersion of the PL energy suddenly appeared at the condensation threshold in a small $k_{\parallel }$ region accompanied by the dispersion of the noncondensate PL as a background. With increasing excitation power density from the threshold, the intensity of the noncondensate PL became negligible. As a result, we found a dispersive profile of the dispersion relation of the condensate in a large $k_{\parallel }$ region in addition to the flat dispersion corresponding to the diffusive profile. The total dispersion relation of the condensate was explained quantitatively by a theoretical model for nonequilibrium condensation.

Figure 1

(a) Angle-resolved reflectance spectra at various incident angles from $\theta =0^{\circ }$ to 60° at 77 K in the CuBr microcavity. (b) Dispersion relations of the cavity polaritons (solid curves) and cavity photon (dashed curve) estimated from analysis of the incident angle dependence of reflectance dip energies (solid circles and squares) with a phenomenological Hamiltonian for the strong coupling. The horizontal dashed lines depict the energies of the $Z_{\mathrm{f}},Z_{1,2}$, and $Z_3$ excitons. (c) Relative fractions of the $Z_{\mathrm{f}},Z_{1,2}$, and $Z_3$ excitons and cavity photon in the LP as a function of $k_{\parallel }$.

Figure 2

Average excitation power-density dependence of the PL spectrum at $k_{\parallel }=0$ at 77 K, where the vertical dashed line indicates the LP energy at $k_{\parallel }=0$ obtained from the reflectance spectrum at $\theta =0^{\circ }$. The inset shows the results of the line-shape analysis of the PL spectra (open circles) above the threshold for the ${\mathrm{B}}_{\mathrm{th}}$-PL band, where the PL intensity is normalized to the maximum value at each excitation power density. The dashed curves indicate the results of decomposition of the PL spectrum with two Gaussian functions corresponding to the ${\mathrm{B}}_{\mathrm{th}}$-PL and LP-PL bands, and the solid curve depicts the sum of the decomposed two bands.

Figure 3

(a) Integrated intensity, (b) FWHM, and (c) peak energy of the LP-PL and ${\mathrm{B}}_{\mathrm{th}}$-PL bands at $k_{\parallel }=0$ as a function of average excitation power density. The green dashed lines in (a) indicate the fitted results of the excitation power-density dependence of the integrated intensity of the LP-PL band.

Figure 4

Image maps of angle-resolved PL spectra at 77 K as a function of $k_{\parallel }$ at various average excitation power densities of (a) 0.5, (b) 3.5, (c) 4.0, and (d) $6.0\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$, where the PL intensity, which is normalized to the maximum intensity at each excitation power density, is indicated by the color scale. The black dashed curve depicts the intrinsic LP dispersion relation taken from Fig. 1.

Figure 5

PL spectra (open circles) at various $k_{\parallel }$ values taken from Fig. 4 at $6.0\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$, where the PL intensity is normalized to the maximum value at each $k_{\parallel }$. The dashed curves indicate the results of decomposition of the PL spectrum with two Gaussian functions corresponding to the ${\mathrm{B}}_{\mathrm{th}}$-PL and LP-PL bands, and the solid curve depicts the sum of the decomposed two bands.

Figure 6

Peak energies of the ${\mathrm{B}}_{\mathrm{th}}$-PL and LP-PL bands (solid and open circles) obtained from the line-shape analysis, which is the same manner as that in Fig. 5, of the PL spectra taken from Fig. 4 at $6.0\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$ as a function of $k_{\parallel }$, where the green solid line indicates the fitted dispersion relation of the LP condensate using Eq. (2), the red dashed line depicts the Bogoliubov-mode dispersion relation given by Eq. (3), and the black solid curve represents the intrinsic LP dispersion relation taken from Fig. 1 for reference. The black dashed curve indicates the result of parabolic fitting of the $k_{\parallel }$ dependence of the LP-PL peak energy.