Polaron Polaritons in the Integer and Fractional Quantum Hall Regimes

Elementary quasiparticles in a two-dimensional electron system can be described as exciton polarons since electron-exciton interactions ensures dressing of excitons by Fermi-sea electron-hole pair excitations. A relevant open question is the modification of this description when the electrons occupy flat bands and electron-electron interactions become prominent. Here, we perform cavity spectroscopy of a two-dimensional electron system in the strong coupling regime, where polariton resonances carry signatures of strongly correlated quantum Hall phases. By measuring the evolution of the polariton splitting under an external magnetic field, we demonstrate the modification of polaron dressing that we associate with filling factor dependent electron-exciton interactions.

Figure 1

Observation of polaron polaritons in a GaAs QW. (a) We couple a 2DES to the optical mode of a microcavity composed of two DBRs. In the strong coupling regime, the lowest energy eigenstates of the coupled system are the lower polariton (LP) and the upper polariton (UP). (b) Reflectivity spectrum of the system as we tune the cavity frequency.

Figure 2

Cavity spectroscopy of the system in the fractional quantum Hall regime, as we tune $B$ for fixed $E_{\mathrm{cav}}$ (white dashed line). Measurement performed with (a) ${\sigma }^{-}$ and (b) ${\sigma }^{+}$ polarized light. (c) Relevant energy levels and optical transitions around $\nu =1$. Because of phase-space filling, creation of a $\mathrm{LL}{0}_e\text{−}\mathrm{LL}{0}_{\mathrm{HH}}$ electron-hole pair is only possible in ${\sigma }^{+}$ polarization (blue arrows). (d) Polariton splitting measured in ${\sigma }^{-}$ (blue) and ${\sigma }^{+}$ (red) polarizations.

Figure 3

Cavity spectroscopy of the system in the fractional quantum Hall regime, as we tune $B$ for fixed $E_{\mathrm{cav}}$ (white dashed line). Measurement performed with (a) ${\sigma }^{-}$ and (b) ${\sigma }^{+}$ polarized light. (c) Relevant energy levels and optical transitions around $\nu =2/5$. Creation of a $\mathrm{LL}{0}_e\text{−}\mathrm{LL}{0}_{\mathrm{HH}}$ electron-hole pair is now possible in both polarizations (blue arrows). Formation of a singlet polaron at $\nu =2/5$ is nevertheless prevented in ${\sigma }^{-}$-polarization, due to the absence of screening ${\mathrm{LL}0}_e$ electrons of opposite spin. (d) Polariton splitting around $\nu =2/5$ measured in ${\sigma }^{-}$ (blue) and ${\sigma }^{+}$ (red) polarizations. (e) Lower polariton (${\mathcal{A}}_{\mathrm{LP}}$) and upper polariton (${\mathcal{A}}_{\mathrm{UP}}$) peak areas in ${\sigma }^{-}$ (blue) and ${\sigma }^{+}$ (red) polarizations (arbitrary units).

Figure 4

Polaron-polariton dispersion around $\nu =2/5$. (a) Cavity spectroscopy at $\nu =0.4$ for different in-plane momenta $k_{\parallel }$ (${\sigma }^{-}$ polarization). The energies are plotted relative to $E_0$, the energy of the $k=0\mu {\mathrm{m}}^{-1}$ lower polariton at $\nu =2/5$. The flat reflection signal observable between the lower and upper polaritons around $k=0{\mu \mathrm{m}}^{-1}$ is an experimental artifact, stemming from an etalon effect in the detection path. (b) Fitted energy of the lower polaron polariton for small $k_{\parallel }$ at filling factor $\nu =0.42$ (green), $\nu =0.4$ (orange), and $\nu =0.37$ (blue). The error bars are statistical errors from Lorentzian fits of the lower polariton line. Dashed lines show parabolic fits to the lower polariton energies.