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arXiv:2004.05559 · Physical Review A

Two-dimensional exciton-polariton interactions beyond the Born approximation

Hui Hu, Hui Deng, Xia-Ji Liu

Published Dec 9, 2022• 5 citations
arXivHTMLPDF

Abstract

We present a many-body theory for the interactions of two-dimensional exciton-polaritons beyond the Born approximation. Taking into account Gaussian quantum fluctuations via the Bogoliubov theory, we find that the exciton-exciton scattering is strongly renormalized by the light-matter coupling and acquires an inverse logarithmic dependence on the lower polariton energy. As a result, the polariton interaction strength may be enhanced at red photon-exciton detuning when the exciton-exciton scattering length is large. We also derive the exact Tan relations for exciton-polaritons, calculate Tan's contact coefficient and find an even more significant enhancement. Our predictions may provide a qualitatively correct guide for studies of exciton and polariton nonlinearities and suggest a route to achieving strongly nonlinear polariton gases.

DOI
10.1103/physreva.106.063303

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We present a many-body theory for the interactions of two-dimensional exciton-polaritons beyond the Born approximation. Taking into account Gaussian quantum fluctuations via the Bogoliubov theory, we find that the exciton-exciton scattering is strongly renormalized by the light-matter coupling and acquires an inverse logarithmic dependence on the lower polariton energy. As a result, the polariton interaction strength may be enhanced at red photon-exciton detuning when the exciton-exciton scattering length is large. We also derive the exact Tan relations for exciton-polaritons, calculate Tan's contact coefficient and find an even more significant enhancement. Our predictions may provide a qualitatively correct guide for studies of exciton and polariton nonlinearities and suggest a route to achieving strongly nonlinear polariton gases.
The hybridization of light and matter excitations in the form of polaritons has enabled major advances in understanding and controlling optical nonlinearities. Entering the quantum regime of strong interactions between individual photons has, however, remained challenging since the strength of achievable polariton interactions is typically limited by the available interactions in the material. Here, we investigate collisions between dark-state polaritons in three-level systems and discover a resonant process that yields effective interactions, which are much larger than the underlying interaction between their matter constituents. We systematically investigate the underlying mechanism and demonstrate a substantial enhancement of polariton interactions by several orders of magnitude. This suggests a promising approach to quantum nonlinear optics in a range of physical settings, from atomic gases to excitons in semiconductors and two-dimensional bilayer materials.
A full quantum theory beyond the mean-field regime is developed for an exciton-polariton condensate, for a complete understanding of quantum fluctuations. We find an analytical solution for the polariton density matrix, showing the nonlinearity causing fast relaxation correlated with the pump so as to yield the quantum condensation above threshold. Increasing the pump intensity, a nonequilibrium phase transition towards the condensation of the lower polaritons emerges, with a statistics transiting from a thermal, through a super-Poissonian, and towards a nonclassical distribution; the latter two possess off-diagonal long-range order but the last one is beyond. The results signify the role of dark states for polariton fluctuations, and lead to a nonclassical counting statistics of emitted photons, which elaborates the role of the key parameters, e.g., pump, detuning, and temperature.
Summary form only given. The role of exciton-exciton scattering in the nonlinear optical response of semiconductor quantum wells is well established. However, an interesting question arising from the system's dimensionality has so far not been addressed. In the quantum theory of scattering in two dimensions, the scattering amplitude behaves non-smoothly and non-perturbatively at low energies. While the exact scattering amplitude vanishes as 1/ln (energy) as energy /spl darr/0, the second Born approximation diverges logarithmically. These properties result from the system's dimensionality and hold for any short-range well-behaved potential. One may ask whether the second Born approximation also fails for exciton-exciton scattering in two-dimensional structures and how this breakdown may be experimentally detected. In this contribution, we address this question within a microscopic theory of frequency-degenerate four-wave-mixing signals from a quantum-well microcavity. Analyzing an experiment reported in with this theory, we argue that the data are already sufficiently sensitive to show the breakdown of the second Born approximation for exciton-exciton scattering.
Semiconductors systems exhibiting excitonic properties are discussed in terms of their coherent response, which is extracted using two-dimensional coherent spectroscopy. This control method allows for separation of quantum pathways that comprise the optical response, such as interactions between excitons, their dephasing rates, the effects of many-body interactions and the role of structure on the microscopic electronic environment. Additional controls, such as polarization can be used to further distinguish biexcitons and suppress many-body interactions. These result are compared and contrasted with those from a semiconductor microcavity where the excitons form polaritonic modes due to normal-mode splitting. Rephrasing spectra map the detuning dependence of the exciton-polariton branches. Increasing the detuning shifts all features to higher energy and the expected anti-crossing is observed. An isolated biexciton is seen only at negative detuning, separated by a binding energy. For positive detuning, the spectral weight of the off-diagonal features swap, as the lower polariton branch and biexciton come into resonance. This indicates that the off-diagonal features are sensitive to the interactions of the exciton-polaritons and other resonances in the system.
Understanding how strong correlations and dissipation combine to shape collective quantum excitations is a central challenge in many-body physics. We investigate the effect of dissipative light-matter coupling on strongly interacting exciton-polaritons in the presence of a biexciton resonance, which gives rise to polaron-polariton quasiparticles. We show that the interplay between many-body correlations and non-Hermitian coupling generates anomalous dispersion relations and exceptional points in the polaron-polariton spectrum. The location and coexistence of exceptional points are controlled by the dissipative coupling and the relative decay rates of the excitonic and photonic constituents, allowing them to emerge across different polaron-polariton branches. These results identify dissipative polaron-polaritons as a versatile platform for exploring non-Hermitian many-body physics with tunable light-matter quasiparticles.
We develop a many-body theory for the properties of exciton-polaritons interacting strongly with a Bose-Einstein condensate (BEC) of exciton-polaritons in another spin state. Interactions lead to the presence of a two-body bound state, the biexciton, giving rise to a Feshbach resonance in the polariton spectrum when its energy is equal to that of two free polaritons. Using the minimal set of terms to describe this resonance, our theory recovers the main findings of two experiments probing interaction effects for upper and lower polaritons in a BEC. This strongly supports that Feshbach physics has, indeed, been realized, and we furthermore extract the energy and decay of the biexciton from the experimental data. The decay rate is predicted to be much larger than that coming from its dissociation into two free polaritons, indicating that other decay channels are important.