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arXiv:1711.08399 · Annalen der Physik

Completely Subradiant Multi‐Atom Architectures Through 2D Photonic Crystals

Fernando Galve, Roberta Zambrini

Published Apr 6, 2018• 5 citations
arXivHTMLPDF

Abstract

Abstract Following recent advances in the manipulation of atoms trapped near 1D waveguides and proposals to use surface acoustic waves on piezoelectric substrates for the same purpose, the potential of two‐dimensional platforms is shown. Directional emission of atoms near photonic crystal slabs with square symmetry is used, in the ideal case, to build perfect subradiant states of 2 distant atoms, possible in 2D only for finite lattices with perfectly reflecting boundaries. These allow the design of massively parallel 1D arrays of atoms above a single crystal, useful for multi‐port output of nonclassical light, by exploiting destructive interference of guided resonance modes. Directionality of the emission is shown to be present whenever a linear iso‐frequency manifold is present in the dispersion relation of the crystal. Multi‐atom radiance properties can be predicted from a simple cross‐talk coefficient of a master equation, in good agreement with exact atom‐crystal dynamics, showing its predictive power. Departing from the ideal theoretical case, possible experimental issues in photonic crystal implementations are also discussed, and an outlook of other relevant modern platforms for 2D propagation of excitations is given.

DOI
10.1002/andp.201800017

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We study coherent and radiative interactions induced among two or more quantum units by coupling them to two-dimensional (2D) lattices acting as structured environments. This model can be representative of atoms trapped near photonic crystal slabs, trapped ions in Coulomb crystals, or to surface acoustic waves on piezoelectric materials, cold atoms on state-dependent optical lattices, or even circuit QED architectures, to name a few. We compare coherent and radiative contributions for the isotropic and directional regimes of emission into the lattice, for infinite and finite lattices, highlighting their differences and existing pitfalls, e.g., related to long-time or large-lattice limits. We relate the phenomenon of directionality of emission with linear-shaped isofrequency manifolds in the dispersion relation, showing a simple way to disrupt it. For finite lattices, we study further details such as the scaling of resonant number of lattice modes for the isotropic and directional regimes, and relate this behavior with known van Hove singularities in the infinite lattice limit. Furthermore, we export the understanding of emission dynamics with the decay of entanglement for two quantum, atomic or bosonic, units coupled to the 2D lattice. We analyze in some detail completely subradiant configurations of more than two atoms, which can occur in the finite lattice scenario, in contrast with the infinite lattice case. Finally, we demonstrate that induced coherent interactions for dark states are zero for the finite lattice.
Abstract Integrating nanophotonics and cold atoms has drawn increasing interest in recent years due to diverse applications in quantum information science and the exploration of quantum many‐body physics. For example, dispersion‐engineered photonic crystal waveguides (PCWs) permit not only stable trapping and probing of ultracold neutral atoms via interactions with guided‐mode light, but also the possibility to explore the physics of strong, photon‐mediated interactions between atoms, as well as atom‐mediated interactions between photons. While diverse theoretical opportunities involving atoms and photons in 1D and 2D nanophotonic lattices have been analyzed, a grand challenge remains the experimental integration of PCWs with ultracold atoms. Here, an advanced apparatus that overcomes several significant barriers to current experimental progress is described, with the goal of achieving strong quantum interactions of light and matter by way of single‐atom tweezer arrays strongly coupled to photons in 1D and 2D PCWs. Principal technical advances relate to efficient free‐space coupling of light to and from guided modes of PCWs, silicate bonding of silicon chips within small glass vacuum cells, and deterministic, mechanical delivery of single‐atom tweezer arrays to the near fields of photonic crystal waveguides.
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We study light scattering off a two-dimensional (2D) array of atoms driven to Rydberg levels. We show that the problem can be mapped to a generalized model of waveguide QED, consisting of multiple 1D photonic channels (transverse modes), each of which directionally coupled to a corresponding Rydberg surface mode of the array. In the Rydberg blockade regime, collective excitations of different surface modes block each other, leading to multi-channel correlated photonic states. Using an analytical approach, we characterize inter-channel quantum correlations, and elucidate the role of collective two-photon resonances of the array. Our results open new possibilities for multimode many-body physics and quantum information with photons in a free-space platform.
Quantum emitters trapped near photonic crystal waveguides have recently emerged as an exciting platform for realizing novel quantum matter-light interfaces. Here, we study tunable photon scattering in a photonic crystal waveguide coupled to an atom dimer with an arbitrary spatial separation. In the weak-excitation regime, we give the energy levels and their decay rates into the waveguide modes in the dressed basis, which both depend on the distance between the two atoms. We focus on the Bragg case and anti-Bragg case, where subradiant and superradiant states are produced and perfect transmission with a $\ensuremath{\pi}$ phase shift may occur on resonance. We observe quantum beats in the photon-photon correlation function of the reflected field in the anti-Bragg case. Moreover, the frequencies of quantum beats can be controlled due to the tunability of the bound states via the dispersion engineering of the structure. We also observe directional photon emission in the anti-Bragg case and give the dynamic mechanism of the perfect transmission. We quantify the effects of the system imperfections, including the deviation in the distance between the two atoms and the asymmetry in the atomic decay rates into the waveguide modes. With recent experimental advances in the superconducting microwave transmission lines, our results should soon be realizable.