Multiple polariton modes originating from the coupling of quantum wells in planar microcavity

We report on the observation of multiple polariton modes, originating from an electronic coupling between quantum wells inside a planar microcavity. A series of excitonic transitions are measured for a bare quantum well stack and are precisely identified to electron-hole transitions originating from the coupling of the wells. When the quantum well stacks are placed at the antinode of a high $Q$-factor microcavity, a series of anticrossings is observed, which is characteristic of a multiplicity of polariton modes. This behavior is simulated using a coupled oscillator model accounting for the cavity mode and all allowed excitonic transitions.

Figure 1

PL spectrum of a stack of three 12 nm ${\mathrm{In}}_{0.03}{\mathrm{Ga}}_{0.97}\mathrm{As}$ QWs with a 10 nm spacer and the corresponding PLE when detecting at the energy of the lowest exciton transition. The inset shows the PL when the excitation laser is at an energy of 1.5 eV.

Figure 2

Calculated wave functions for bound electron $e_i$ and heavy hole $h{h}_i$ states. The black lines show schematically the positions of the potential barriers. An offset between wave functions is introduced to distinguish different states and the amplitude is not to scale. The integer $i$ indicates an increase (decrease) in energy for electrons (holes) and corresponds to ($i-1$) nodes of the eigenfunction.

Figure 3

Energy of electron-hole transitions relative to the first transition $E_{e1-hh1}$ for the bare QW sample (red), calculated for a single QW stack (black), and the relative values used for the strong coupling model (blue). The relative value for the $e_3-h{h}_1$ and $e_3-h{h}_5$ are shown for comparison. The label $1-lh$ indicate the transition from $e_1$ to the light hole.

Figure 4

(a) PL intensity map in log scale as a function of the position on the microcavity sample. (b) PL spectra for three positions on the sample as indicated by the dashed lines in (a). The arrow indicates the doublet of peaks at 1.489 eV.

Figure 5

Polariton energy as a function of sample position. The dots show the extracted peak energy and the gray regions show the uncertainty for each state. The red full lines shows the best fits using Eqs. (1) and (2) in (a) or by manually adjusting the overlap parameter in (b). The dashed lines represent the energy of the cavity mode (parabola) and exciton transitions (straight). In both cases, the coupling parameter is ${\mathrm{\Omega }}_0=4$ meV and the values of the the overlap integrals are given in Table 1.