Coherent optical control of the wave function of zero-dimensional exciton polaritons

Control of the wave function of confined microcavity polaritons is demonstrated experimentally and theoretically by means of tailored resonant optical excitation. Three dimensional confinement is achieved by etching mesas on top of the microcavity spacer layer. Resonant excitation with a continuous-wave laser locks the phase of the discrete polariton states to the phase of the laser. By tuning the energy and momentum of the laser, we achieve precise control of the momentum pattern of the polariton wave function. This is an efficient and direct way for quantum control of electronic excitations in a solid.

Figure 1

(Color online) (a) Real space spectrum of a $9\mu \text{m}$ mesa at 2 meV negative detuning; upper and lower polariton branches of the 2D and 0D polaritons are clearly visible. (b) $K$-space images of resonantly excited states from the 0D lower polariton branch. The states can be labeled with two quantum numbers $\left(n,m\right)$. $2\left|m\right|$ gives the number of nodes along $\varphi$ on a full circle, while $n$ corresponds to the number of lobes in radial direction.

Figure 2

(Color online) Lobes of the degenerate second doublet state in a $3\mu \text{m}$ mesa following the rotation of the laser in $k$ space. The mesa was at zero detuning. The upper part shows the experimental results and the theoretical results from the simulation are shown in the lower part of the figure. The high intensity spot which is visible in each experimental image of this figure is an emission maximum arising from the laser light transmitted directly through the cavity beside the mesa. This makes it easy to observe the excitation angle. In the simulation images the laser position is marked by a circle.

Figure 3

(Color online) Manipulation of the wave functions of the split first doublet in a $3\mu \text{m}$ mesa ($\approx 3\text{meV}$ negative detuning) by changing the excitation energy while keeping the excitation point constant. Upper part: experiment; lower part: theoretical results. The polariton lifetime in our sample is about 15 ps, which leads to an energy linewidth of the eigenstates much broader than the spectral width of the laser. The lobes rotate due to the different contributions of the eigenstates to the linear response.