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Long-range interactions in Weyl photonic crystals

Lei Ying, Ming Zhou, Michael Sabatini Mattei, Boyuan Liu, Paul J. Campagnola, Randall H. Goldsmith, Zongfu Yu

Published Jun 19, 2019• 0 citations
OpenAlex

Abstract

The interaction between quantum two-level systems is typically short-range in free space and most photonic environments. Here we show that Weyl photonic crystals can create significantly extended long-range interaction between distant quantum systems because of their diminishing momentum isosurfaces with equal frequencies around isolated Weyl points. The extended range of interaction is robust and does not rely on specific location or orientation of the transition dipoles. A general relation between the interaction range and properties of the isosurface is described, which provides a recipe to identify other photonic environments for that enable long-range interaction. This work lays the foundation to use Weyl photonic crystals as a platform to mediate quantum behavior.

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The interaction between quantum two-level systems is typically short-range in free space and most photonic environments. Here we show that Weyl photonic crystals can create significantly extended long-range interaction between distant quantum systems because of their diminishing momentum isosurfaces with equal frequencies around isolated Weyl points. The extended range of interaction is robust and does not rely on specific location or orientation of the transition dipoles. A general relation between the interaction range and properties of the isosurface is described, which provides a recipe to identify other photonic environments for that enable long-range interaction. This work lays the foundation to use Weyl photonic crystals as a platform to mediate quantum behavior.
The interaction between quantum two-level systems is typically short range in free space and in most photonic environments. We show that diminishing momentum isosurfaces with equal frequencies can create a significantly extended range of interaction between distant quantum systems. The extended range is robust and does not rely on a specific location or orientation of the transition dipoles. A general relation between the interaction range and properties of the isosurface is described for structured photonic media. It provides a new way to mediate long-range quantum behavior.
Weyl photons appear when two three-dimensional photonic bands with linear dispersion are degenerate at a single momentum point, labeled as Weyl point. These points have remarkable properties such as being robust topological monopoles of Berry curvature as well as an associated vanishing density of states. Here, we study the quantum optical consequences of such topological Weyl photons by characterizing the individual and collective dynamics of quantum emitters close to resonance with these points. Using an exact non-perturbative treatment, we predict the development of non-exponential decay dynamics due to the emergence of localized photonic states around the emitters. We find that these bound states, whose wavefunction displays power-law spatial decay, can mediate coherent and topological long-range interactions when many emitters exchange energy through Weyl photons. Furthermore, by exploiting the topological protection of Weyl points, we provide a recipe to tune the range of the mediated interactions while keeping their power-law nature, something not possible in any other photonic platform. Thus, Weyl photons enable coherent, tunable, long-range interactions between emitters, and therefore can become a very valuable platform in the context of quantum simulation.
Enhancing the radiative interaction between quantum electronic transitions is of general interest. There are two important properties of radiative interaction: the range and the strength. There has been a trade-off between the range and the strength observed in the literature. Such apparent trade-off arises from the dispersion relation of photonic environments. A general recipe is developed to overcome such trade-off and to simultaneously enhance the range and the strength of radiative interactions.
New paradigms for optical physics emerge with lattices of atoms trapped in one and two-dimensional photonic crystals [1-4]. Exemplary experimental platforms include photonic crystal waveguides [5-7] and cavities [8, 9]. Owing to their small optical loss and tight field confinement, these nanoscale dielectric devices are capable of mediating long-range atom-atom interactions using photons propagating in their guided modes. In a complimentary fashion, long-range interactions between photons can be mediated by an underlying lattice of atoms. Such systems have the potential to provide new tools for scalable quantum networks, quantum phases of light and matter, and quantum metrology. However, bringing this future of atom nanophotonics to fruition requires the creation of an interdisciplinary toolkit for the control, manipulation, and interaction of atoms and photons with a complexity and scalability not currently possible. I will give an overview of the theoretical prospects for new physics and review experimental progress in this nascent field at the interfaces of nano-photonics, atomic physics, and quantum optics.
Weyl photons appear when two three-dimensional photonic bands with linear dispersion are degenerate at a single momentum point, labeled as Weyl point. These points have remarkable properties such as being robust topological monopoles of Berry curvature as well as an associated vanishing density of states. In this work, we report on a systematic theoretical study of the quantum optical consequences of such Weyl photons. First, we analyze the dynamics of a single quantum emitter coupled to a Weyl photonic bath as a function of its detuning with respect to the Weyl point and study the corrresponding emission patterns, using both perturbative and exact treatments. Our calculations show an asymmetric dynamical behavior when the emitter is detuned away from the Weyl frequency, as well as different regimes of highly collimated emission, which ultimately translate in a variety of directional collective decays. Besides, we find that the incorporation of staggered mass and hopping terms in the bath Hamiltonian both enriches the observed phenomenology and increases the tunability of the interaction. Finally, we analyze the competition between the coherent and dissipative components of the dynamics for the case of two emitters and derive the conditions under which an effective interacting spin model description is valid.