Ultrastrong Light-Matter Coupling Regime with Polariton Dots

The regime of ultrastrong light-matter interaction has been investigated theoretically and experimentally, using zero-dimensional electromagnetic resonators coupled with an electronic transition between two confined states of a semiconductor quantum well. We have measured a splitting between the coupled modes that amounts to 48% of the energy transition, the highest ratio ever observed in a light-matter coupled system. Our analysis, based on a microscopic quantum theory, shows that the nonlinear polariton splitting, a signature of this regime, is a dynamical effect arising from the self-interaction of the collective electronic polarization with its own emitted field.

Figure 1

(a) Semiconductor quantum well (QW) with two subbands of energies $E_1$ and $E_2$. (b) In-plane parabolic dispersion of the energy subbands, with a sketch of the action of the polarization operator $b^{†}$ (arrows). $E_F$ is the Fermi level. (c) Multiple QWs embedded in a square-shaped microcavity.

Figure 2

(a) Schematics of the QW media of our samples. The first two electronic transitions are $E_2-E_1=12.4\mathrm{meV}$ (3 THz) and $E_3-E_2=19.9\mathrm{meV}$ (4.8 THz). (b) Electronic microscope image of the cleaved facet of an array of metal-dielectric-metal patch cavities. (c) Contour plot of the QW multipass absorption as a function of the frequency and temperature, revealing the first $1\to 2$ and the second $2\to 3$ QW transitions. (d) Reflectivity contour plot, with $\theta =45°$, as a function of frequency and temperature, for a cavity ($s=12.5\mu \mathrm{m}$) with ${\omega }_c=3\mathrm{THz}$, resonant with the $1\to 2$ QW transition.

Figure 3

(a) Reflectivity spectra for different cavities with decreasing size $s$, for an incident angle $\theta =10°$. Spectra have been offset for clarity. The inset summarizes the frequency of the cavity mode as a function of $1/s$ measured at 10° (red triangles) and 45° (blue dots) angles of incidence. (b) Low temperature ($T=4.5\mathrm{K}$) reflectivity spectra $\theta =10°$, for the same cavities as in (a). The minimal polariton separation is the Rabi splitting $2{\Omega }_R=1.41\mathrm{THz}$.

Figure 4

(a) The two polariton peaks ${\omega }_{\mathrm{UP}}$ and ${\omega }_{\mathrm{LP}}$ (in blue) as a function of the plasma frequency ${\omega }_P$, in the resonant case ${\omega }_c={\omega }_{12}$. We have also plotted the energy of the intersubband plasmon, as derived from the absorption experiments (triangles) and Eq. (2) (dashed line). (b) Polaritons frequencies ${\omega }_{\mathrm{UP}}$ and ${\omega }_{\mathrm{LP}}$ as a function of the cavity frequency ${\omega }_c$. The dots are experimental results, and the continuous lines are the roots of Eq. (6) with $f_w=0.62$ and ${\omega }_P=1.8\mathrm{THz}$. The hatched zone indicates the polariton gap.