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Multiple perfectly-transmitting states of a single-level at strong coupling

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 Added by Robert Whitney S.
 Publication date 2019
  fields Physics
and research's language is English




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We study transport through a single-level system placed between two reservoirs with band-structure, taking strong level-reservoir coupling of the order of the energy-scales of these band-structures. An exact solution in the absence of interactions gives the nonlinear Lamb shift. As expected, this moves the perfectly-transmitting state (the reservoir state that flows through the single-level without reflection), and can even turn it into a bound-state. However, here we show that it can also create additional pairs of perfectly-transmitting states at other energies, when the coupling exceeds critical values. Then the single-levels transmission function resembles that of a multi-level system. Even when the discrete level is outside the reservoirs bands, additional perfectly-transmitting states can appear inside the band when the coupling exceeds a critical value. We propose observing the bosonic version of this in microwave cavities, and the fermionic version in the conductance of a quantum dot coupled to 1D or 2D reservoirs.



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Rooted in quantum optics and benefiting from its well-established foundations, strong coupling in nanophotonics has experienced increasing popularity in recent years. With nanophotonics being an experiment-driven field, the absence of appropriate theoretical methods to describe ground-breaking advances has often emerged as an important issue. To address this problem, the temptation to directly transfer and extend concepts already available from quantum optics is strong, even if a rigorous justification is not always available. In this Review we discuss situations where, in our view, this strategy has indeed overstepped its bounds. We focus on exciton--plasmon interactions, and particularly on the idea of calculating the number of excitons involved in the coupling. We analyse how, starting from an unfounded interpretation of the term N/V that appears in theoretical descriptions at different levels of complexity, one might be tempted to make independent assumptions for what the number N and the volume V are, and attempt to calculate them separately. Such an approach can lead to different, often contradictory results, depending on the initial assumptions (e.g. through different treatments of $V$ as the -- ambiguous in plasmonics -- mode volume). We argue that the source of such contradictions is the question itself -- How many excitons are coupled?, which disregards the true nature of the coupled components of the system, has no meaning and often not even any practical importance. If one is interested in validating the quantum nature of the system -- which appears to be the motivation driving the pursuit of strong coupling with small N -- one could instead focus on quantities such as the photon emission rate or the second-order correlation function.
Engineering light-matter interactions up to the strong-coupling regime at room temperature is one of the cornerstones of modern nanophotonics. Achieving this goal will enable new platforms for potential applications such as quantum information processing, quantum light sources and even quantum metrology. Materials like transition metal dichalcogenides (TMDC) and in particular tungsten disulfide (WS$_2$) possess large transition dipole moments comparable to semiconductor-based quantum dots, and strong exciton binding energies allowing the detailed exploration of light-matter interactions at room temperature. Additionally, recent works have shown that coupling TMDCs to plasmonic nanocavities with light tightly focused on the nanometer scale can reach the strong-coupling regime at ambient conditions. Here, we use ultra-thin single-crystalline gold nanodisks featuring large in-plane electromagnetic dipole moments aligned with the exciton transition-dipole moments located in monolayer WS$_2$. Through scattering and reflection spectroscopy we demonstrate strong coupling at room temperature with a Rabi splitting of $sim$108 meV. In order to go further into the strong-coupling regime and inspired by recent experimental work by Stuhrenberg et al., we couple these nanodisks to multilayer WS$_2$. Due to an increase in the number of excitons coupled to our nanodisks, we achieve a Rabi splitting of $sim$175 meV, a major increase of 62%. To our knowledge, this is the highest Rabi splitting reported for TMDCs coupled to open plasmonic cavities. Our results suggest that ultra-thin single-crystalline gold nanodisks coupled to WS$_2$ represent an exquisite platform to explore light-matter interactions.
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