Accelerating Polaritons with External Electric and Magnetic Fields

It is widely assumed that photons cannot be manipulated using electric or magnetic fields. Even though hybridization of photons with electronic polarization to form exciton-polaritons has paved the way to a number of groundbreaking experiments in semiconductor microcavities, the neutral bosonic nature of these quasiparticles has severely limited their response to external gauge fields. Here, we demonstrate polariton acceleration by external electric and magnetic fields in the presence of nonperturbative coupling between polaritons and itinerant electrons, leading to formation of new quasiparticles termed polaron-polaritons. We identify the generation of electron density gradients by the applied fields to be primarily responsible for inducing a gradient in polariton energy, which in turn leads to acceleration along a direction determined by the applied fields. Remarkably, we also observe that different polarization components of the polaritons can be accelerated in opposite directions when the electrons are in $\nu =1$ integer quantum Hall state.

Popular Summary

Light is the backbone of today’s communication network. While processing of classical or quantum information is typically realized in the electronic domain and has witnessed several breakthroughs in recent years, photons have consistently been used as a reliable communication medium. However, if we could manipulate photons by external electric and magnetic fields, as we do very successfully with electrons, this would enable the paradigm of all-optical information processing. Here, we leverage the hybridization of photons with electronic excitations in a solid in order to improve our ability to control photons.

We start with excitons, which are hydrogenlike bound states of an electron and a hole in a solid. Excitons can hybridize with photons to form what we call polaritons and at the same time interact with surrounding electrons. This creates the crucial link, which allows us to manipulate photons by exerting forces on electrons.

We tailor the surrounding electrons into regions with higher and lower electron density using electric and magnetic fields. The attraction between excitons and electrons accelerates the polaritons towards the high-density regions. Because polaritons eventually decay back into photons, the electron profile is directly imprinted onto the photons. The situation is further enriched when electrons enter the quantum Hall regime, where electron charge and spin densities are intertwined. There, the direction of the force depends on photon spin.

One question motivated by our work is whether it is possible to realize a Lorentz force on photons using external electric and magnetic fields. Such tunable photonic gauge fields could play a key role in the realization of strongly correlated states of photons.

Figure 1

Electrical and optical properties of the sample. (a) Layout of the Hall bar and the contacts. (b) Side view of the Hall bar. The top mirror has been etched to contact the 2DEG located in the center QW [doping quantum wells (DQW)]. (c) Current-voltage characteristic of the device where $V_R$ acts as current source and $V_L$ as drain. (d) Map of the lower polariton PL wavelength measured at normal incidence ($k_{\parallel }=0$).

Figure 2

Electrically controlled polariton landscape. (a) Normalized white-light reflectivity spectra showing the polaron-polariton dispersion at the nominal electron density. (b) Exciton-polariton dispersion in the depleted regime ($\mathrm{\Delta }{V}_L=-6\mathrm{V}$). Dashed lines are coupled oscillators fits to the data. (c),(d) Normalized white-light reflectivity spectra at $k_{\parallel }=1.2{\mu \mathrm{m}}^{-1}$ [vertical line in (a) and (b)] as a function of position with a negative bias voltage applied to the left contact $(\mathrm{\Delta }{V}_L=-2.4\mathrm{V})$ (c) and to the right contact $(\mathrm{\Delta }{V}_R=-2.4\mathrm{V})$ (d).

Figure 3

Polariton acceleration in external electric and magnetic fields. (a) Normalized difference between two RF images of polariton flow in opposing electron density gradients. (b) Comparison with a trajectory-based model (dashed green line). The red and blue line is a line cut of (a) at $y=25\mu \mathrm{m}$ and the black line is an average between $y=10$ and $y=40\mu \mathrm{m}$. (c)–(f) Normalized difference between images $I_R$, $I_L$ as in (a) for magnetic fields: (c) $B=8\mathrm{mT}$, (d) $B=-8\mathrm{mT}$ (e), $B=40\mathrm{mT}$, and (f) $B=-40\mathrm{mT}$. The horizontal dash-dotted lines in (a),(c)–(f) delimit the width of the Hall bar, the large circle is the field of view of the microscope, and the central gray disk is the excitation spot.

Figure 4

Spin-selective polariton acceleration. (a) Normalized white-light reflectivity spectra measured at $k_{\parallel }=1.2{\mu \mathrm{m}}^{-1}$ as a function of magnetic field. The corresponding Landau level filling factor is determined from an independent magnetotransport measurement. (b) Normalized reflectivity spectra at $k_{\parallel }=1.2{\mu \mathrm{m}}^{-1}$ and $B=1.1\mathrm{T}$ across the vertical $y$ direction on the Hall bar, with a source-drain bias $\mathrm{\Delta }{V}_R=-0.17\mathrm{V}$. Black points indicate the electron spin polarization $S_z$ measured at three different positions. (c),(d) Momentum-resolved polariton RF emission under cross-linear polarization at 1523.8 meV $(813.62\mathrm{nm})$ for (c) $\mathrm{\Delta }{V}_R=-0.17\mathrm{V}$ and (d) $\mathrm{\Delta }{V}_L=-0.35\mathrm{V}$. The red dashed lines are guides to the eye. (e),(f) Normalized difference between two RF images of right-propagating polaritons acquired with $\mathrm{\Delta }{V}_R=-0.17\mathrm{V}$ and $\mathrm{\Delta }{V}_L=-0.35\mathrm{V}$. (e) Excitation of ${\sigma }^{-}$ polaritons at $k_x=-0.9{\mu \mathrm{m}}^{-1}$, $k_y=0$. (f) Excitation of ${\sigma }^{+}$ polaritons at $k_x=-1.3{\mu \mathrm{m}}^{-1}$, $k_y=0$. The horizontal dash-dotted lines delimit the width of the Hall bar, the large circle is the field of view of the microscope. The red and blue rings in (c)-(f) show the excitation spots in real and momentum spaces for ${\sigma }^{+}$ and ${\sigma }^{-}$ polaritons, respectively.