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# Polaritons in two-dimensional Systems

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The interaction of matter excitations with light confined in an optical cavity forms the basis of cavity quantum electrodynamics. When this interaction exceeds the individual decay rates, exciton-polaritons, composite quasiparticles formed by excitons strongly coupled to the cavity light field, emerge as the new eigenstates of the system. These particles inherit fascinating physical properties from their constituents, and allow for observation of superfluidity and Bose-Einstein condensation at elevated temperatures. Moreover, current fabrication techniques allow to tailor their potential landscape, which makes them promising candidates for quantum simulation of nonequilibrium many-body systems. However, all experiments to date can be described in a mean-field approach due to the weak electron exchange-dominated interaction between exciton-polaritons. Hence, it has been a long-standing goal to demonstrate single-particle nonlinearities in exciton-polariton systems. Research in our group focuses on exploiting different approaches to increase and observe such strong polariton interactions.

One possibility to significantly enhance interactions between polaritons is the introduction of additional transverse confinement either of the excitonic or the photonic part of the polaritonic wavefunction. In analogy to photon blockade, for strong enough interactions one expects polariton blockade, a regime in which the system can only accommodate a single polariton at a time

We use a semi-integrated and fully tunable fiber cavity to couple the intra-cavity light field to excitons in a MBE-grown quantum well. Due to the high reflectivity of the distributed Bragg reflectors and the plane-convex geometry we combine long cavity lifetimes and strong transverse polariton confinement which is crucial to achieve sizable interactions. Moreover, the system exhibits intriguing quantum interference phenomena that can be exploited to generate strongly correlated photons even with small interaction strengths.

In another approach we combine the physics of correlated many-body states of a two-dimensional electron system with the methods of cavity quantum electrodynamics. By coupling the cavity photon of an AlGaAs/GaAs-based two-dimensional DBR microcavity structure to optical interband excitations of a 20nm GaAs quantum well hosting a degenerate electron gas we observe the emergence of novel many-body polariton modes. In the absence of a magnetic field we find trion- polaritons and provide a new interpretation of these modes as optical many-body excitations at the Fermi-edge that are strongly coupled to the cavity photon. In presence of a magnetic field we use the strong coupling of the cavity mode to bound trion states of inter Landau level transitions as a new spectroscopic tool to study correlated states in the integer and fractional quantum Hall regime. These quantum Hall polaritons provide a direct way to study the spin-polarization of quantum Hall states by measuring the polarization-dependent normal-mode splitting. The system is potentially of interest for realizing strongly correlated photonic systems since it may be possible to exploit the strong electron density dependence of 2DEG-polariton splitting, or equivalently the trion Bohr radius, to enhance polariton-polariton interactions.

Another research direction focuses on generation of effective Gauge fields for microcavity polaritons. One approach to achieving this goal is to simultaneously apply perpendicular electric and magnetic fields. The neutral exciton, under strong magnetic field has an electric dipole moment that is perpendicular to its group velocity. Thus an applied electric field will modify the dispersion relation for excitons (hence polaritons) and lead to an additional finite group velocity perpendicular to the applied fields. In the device sketched on the right, we expect a stationary polariton cloud (dashed circle on the right) to pick-up a group velocity that is determined by the electric and magnetic fields. Finite electric field gradient in such a structure should induce an effective gauge field for the polaritons whose strength is controlled by the electric and magnetic fields.