Signatures of the ultrastrong light-matter coupling regime

In a microcavity, light-matter coupling is quantified by the vacuum-Rabi frequency ${\Omega }_R$. When ${\Omega }_R$ is larger than radiative and nonradiative loss rates, the system eigenstates (polaritons) are linear superposition of photonic and electronic excitations, a condition actively investigated in diverse physical implementations. Recently, a quantum electrodynamic regime (ultrastrong coupling) was predicted when ${\Omega }_R$ becomes comparable to the transition frequency. Here we report signatures of this regime in a quantum-well intersubband microcavity. Measuring the cavity-polariton dispersion in a room-temperature linear optical experiment, we directly observe the antiresonant light-matter coupling and the photon-energy renormalization of the vacuum field.

Figure 1

(Color) Difference from the full-Hamiltonian eigenvalues of the polariton energies calculated either without the $H_{\text{antires}}$ terms (red) or without both $H_{\text{antires}}$ and $H_{\text{dia}}$ (blue) plotted as a function of coupling strength (solid and dashed lines refer to the lower and upper polariton branch, respectively). This calculation was performed considering a fixed resonant angle of $60°$. As one can see, deviations amount to $\sim 5\%$ already for ${\Omega }_R/{\omega }_{12}\sim 0.12$.

Figure 2

(Color) Scheme of the experimental setup employed for the angle-resolved reflectance measurements. The prism-shaped sample is mounted on a copper block and can be rotated to vary the internal incidence angle. The blown up detail of the waveguide illustrates the working principle of the resonator. The band profile and squared moduli of the subband envelope functions of one of the quantum wells (calculated solving self-consistently the Poisson-Schrödinger equation) are shown in the top left diagram.

Figure 3

(Color online) Panel (a): root-mean-square deviation from the measured dispersion of the calculated polariton energies as a function of the vacuum-Rabi energy, the only fitting parameter. The red dashed curve refers to the case of no $H_{\text{antires}}$ terms, while the blue dash-dotted to the case without both $H_{\text{dia}}$ and $H_{\text{antires}}$ contributions. The black line is for the full Hamiltonian. Bottom panels: angular dispersions of the lower (b) and upper (c) polaritons in the three cases (full Hamiltonian for the black solid line, without $H_{\text{antires}}$ for the red dashed line, and without both $H_{\text{dia}}$ and $H_{\text{antires}}$ for the blue dash-dotted line) compared to experimental data (black crosses). The experimental errors have been found to be negligible (below 1 meV) and are thus not shown. The ${\Omega }_R$ used are the ones that minimize the root-mean-square deviation in panel (a).