Electrically controlled mutual interactions of flying waveguide dipolaritons

We show that, with a system of electrically gated wide quantum wells embedded inside a simple dielectric waveguide structure, it is possible to excite, control, and observe waveguided exciton polaritons that carry an electric dipole moment. We demonstrate that the energy of the propagating dipolariton can be easily tuned using local electrical gates, that their excitation and extraction can be easily done using simple evaporated metal gratings, and that the dipolar interactions between polaritons and between polaritons and excitons can also be controlled by the applied electric fields. This system of gated flying dipolaritons thus exhibits the ability to locally control both the single polariton properties as well as the interactions between polaritons, which should open up opportunities for constructing complex polaritonic circuits and for studying strongly interacting, correlated polariton gases.

Figure 1

(a) An illustration of the experimental scheme. A nonresonant excitation through a thin Ti electrode is used to excite polaritons which propagate with a propagation constant $\beta$. A gold grating coupler with a periodicity of 240 nm is used to read out the signal. (b) Numerical calculation of the expected dispersion from our device in the absence of an electric field. The bare heavy hole $\left(X_{hh}\right)$ and light hole $\left(X_{lh}\right)$ excitons are marked as well as The LP, MP, and UP polariton branches. The bare WG mode is illustrated by the dashed line. (c) Calculations of the charge distribution along the growth direction for $F=0$, 12, and 22 kV/cm. (The nonuniform distribution when $\mathbf{F}=0$ originates from the mass difference between the electron and the hole which makes the electron wave function more extended.) (d) Calculations of the exciton redshift and effective dipole length as a function of $\mathbf{F}$.

Figure 2

(a)-(c) The measured dispersion at three different values of $\mathbf{F}$ (measured at 30 K), fitted with a coupled oscillator model (dashed). A red shift of the entire polaritonic dispersion as $\mathbf{F}$ increases can be clearly seen. (d) The energies of the LP (below the avoided crossing point, marked by the white dots in (a-c)) and of the $X_{hh}$ as a function of $\mathbf{F}$. (e) The measured (blue dots) and calculated (red line) Rabi frequency ratio, ${\mathrm{\Omega }}_p^{hh}\left(F\right)/{\mathrm{\Omega }}_p^{hh}\left(0\right)$, as function of $\mathbf{F}$.

Figure 3

(a) Measured dispersion at different excitation powers and different values of $\mathbf{F}$ (measured at 5 K). Each row represents a constant $\mathbf{F}$ while each column represents a constant excitation power. The increased energy blueshift $\left(\mathrm{\Delta }E\right)$ with increasing power is clearly seen, and is more significant at larger $\mathbf{F}$ values. The TM mode is marked by an arrow in the top left panel. (b) The energy blueshift, $\mathrm{\Delta }E$, measured where ${\chi }_x=\frac{1}{2}$ [marked by the black points on (a)] as a function of the LP emission intensity, for three different values of $\mathbf{F}$. (c) An estimation for the density of the dipoles extracted from the $\mathrm{\Delta }E$ values in (b) using the mean field model. The value of the effective dipole for a selected point on each of the three curves is marked.

Figure 4

Layer structure of the measured sample.

Figure 5

The experimental setup.

Figure 6

RCWA numerical calculations of our sample. (a) Calculated dispersion for TE (left panel) and TM (right panel) polarizations. The $X_{hh}$ and $X_{lh}$ are marked as well as the first and second WG modes at each polarization. The difference between the dispersions of the TE and the TM polaritons can be seen. (b) The distribution of the electromagnetic field in one unit cell, calculated for the marked point in the top left panel.

Figure 7

The probability distribution of the electron and the heavy hole at (a) $F=0$ and (b) $F=22$ kV/cm calculated using our self-consistent Schrödinger-Poisson solver.

Figure 8

Normalized PL at 30 K (left) and 5 K (right).