Nonlinear optics in the fractional quantum Hall regime

Abstract

These authors contributed equally to this work.Engineering strong interactions between optical photons is a great challenge for quantum science. Envisioned applications range from the realization of photonic gates for quantum information processing [1] to synthesis of photonic quantum materials for investigation of strongly-correlated drivendissipative systems [2]. Polaritonics, based on the strong coupling of photons to atomic or electronic excitations in an optical resonator, has emerged as a promising approach to implement those tasks [3]. Recent experiments demonstrated the onset of quantum correlations in the exciton-polariton system [4,5], showing that strong polariton blockade [6] could be achieved if interactions were an order of magnitude stronger. Here, we report time resolved four-wave mixing experiments on a two-dimensional electron system embedded in an optical cavity [7], demonstrating that polariton-polariton interactions are strongly enhanced when the electrons are initially in a fractional quantum Hall state. Our experiments indicate that in addition to strong correlations in the electronic ground state, exciton-electron interactions leading to the formation of polaron polaritons [8-11] play a key role in enhancing the nonlinear optical response. Besides potential applications in realization of strongly interacting photonic systems, our findings suggest that nonlinear optical measurements could provide information about fractional quantum Hall states that is not accessible in linear optical response.Polaritons have recently attracted considerable interest, motivated by the fact that their interactions can be engineered almost at will through the tunability of their matter component. For example, strongly interacting Rydberg polaritons have recently been obtained using the nonlinear behavior of Rydberg excitations in an ensemble of atoms [12], which led to the demonstration of Rydberg polariton blockade [13] where the presence of a single polariton in a well-delimited region of space prevents the resonant injection of other polaritons. In parallel, efforts are being made to realize polariton blockade in condensed matter systems that hold great potential for realizing compact and integrated synthetic quantum materials [3]. Exciton polaritons in semiconductor materials are part light part matter particles that arise from the strong coupling of a quantum well exciton and a cavity photon [14]. These photonic particles inherit a nonlinear behavior from exciton-exciton interactions [2,15,16]. For efficient blockade to be obtained, the nonlinearity U needs to be greater than the inverse lifetime γ of the polaritons [6]. Recent state-of-the art experiments based on photon correlation measurements in semi-integrated microcavities attained optimized values of the ratio U/γ 0.1 in a photonic dot with about 3 µm 2 area [4,5]. These experiments represent the culmination of decade long technological developments aimed at increasing U/γ through reducing the photonic mode area [17][18][19] as well as increasing t...

Optical excitations in compressible and incompressible two-dimensional electron liquids

“…In this way, we find a repulsive interaction between excitons, but the strength of these interactions shows no dependence on the filling factor. This result disagrees with recent experimental observations 20 where some incompressible phases exhibit enhanced nonlinearities. This discrepancy may be due to the idealizations of our theoretical model in which we assume full spin polarization and disregard Landau level mixing.…”

Polariton panorama

“…investigated cavity exciton polaritons in the presence of high-mobility 2D electron gas subjected to external magnetic field and discovered novel correlated electron phases. Knuppel et al [467] reported on strong polariton-polariton interactions in the fractional quantum Hall regime.…”

Thomas–Reiche–Kuhn (TRK) sum rule for interacting photons

“…Following the same reasoning, it can also be shown that also the f-sum rule [16] (the longitudinal analog of the TRK sum rule) for an electron system strongly interacting with a quantized electromagnetic field can be obtained. These sum rules can find useful applications in the study of correlated electron systems strongly interacting with photons (see, e.g., [76]).…”