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arXiv:1705.07883 · Physical Review A

Coherent and radiative couplings through two-dimensional structured environments

Fernando Galve, Roberta Zambrini

Published Mar 23, 2018• 12 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.97.033846

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Physical Review Letters•Dec 1, 2017•0 citations
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 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.
Spontaneous emission is one of the most fundamental out-of-equilibrium processes in which an excited quantum emitter relaxes to the ground state due to quantum fluctuations. In this process, a photon is emitted that can interact with other nearby emitters and establish quantum correlations between them, e.g., via super and subradiance effects. One way to modify these photon-mediated interactions is to alter the dipole radiation patterns of the emitter, e.g., by placing photonic crystals near them. One recent example is the generation of strong directional emission patterns - key to enhancing super and subradiance effects - in two dimensions by employing photonic crystals with band structures characterized by linear isofrequency contours and saddle points. However, these studies have predominantly used oversimplified toy models, overlooking the electromagnetic field's intricacies in actual materials, including aspects like geometrical dependencies, emitter positions, and polarization. Our study delves into the interaction between these directional emission patterns and the variables mentioned above, revealing the untapped potential to fine-tune collective quantum optical phenomena.
Spontaneous emission is one of the most fundamental out-of-equilibrium processes in which an excited quantum emitter relaxes to the ground state due to quantum fluctuations. In this process, a photon is emitted that can interact with other nearby emitters and establish quantum correlations between them, e.g., via super and subradiance effects. One way to modify these photon-mediated interactions is to alter the dipole radiation patterns of the emitter, e.g., by placing photonic crystals near them. One recent example is the generation of strong directional emission patterns-key to enhancing super and subradiance effects-in two dimensions by employing photonic crystals with band structures characterized by linear isofrequency contours and saddle-points. However, these studies have predominantly used oversimplified toy models, overlooking the electromagnetic field's intricacies in actual materials, including aspects like geometrical dependencies, emitter positions, and polarization. Our study delves into the interaction between these directional emission patterns and the aforementioned variables, revealing the untapped potential to fine-tune collective quantum optical phenomena.
We present a framework to investigate the collective properties of atomic lattices in one, two, and three dimensions. We analyze the single-photon band structure and associated atomic decay rates, revealing a fundamental dependence on dimensionality. One- and two-dimensional arrays are shown to be inherently radiative, exhibiting band gaps and decay rates that oscillate between superradiant and subradiant regimes, as a function of lattice spacing. In contrast, three-dimensional lattices are found to be fundamentally non-radiative due to the inhibition of spontaneous emission, with decay only at discrete Bragg resonances. Furthermore, we demonstrate that this structural difference dictates the system dynamics, which crosses over from dissipative decay in lower dimensions to coherent transport in three dimensions. Our results provide insight into cooperative effects in atomic arrays at the single-photon level.
Recent advances are enabling quantum emitters to interact with photonic crystals, whose electromagnetic modes exhibit complex dispersion relations, spatial mode structure, and polarization textures. However, modeling light-matter behavior in these systems faces a persistent trade-off: electromagnetic approaches based on Maxwell-equation solvers provide realistic vectorial descriptions but are difficult to integrate with quantum many-body and non-perturbative methods, whereas simplified quantum-optical lattice models are tractable but typically rely on scalar and spatially independent light-matter couplings that miss essential features of these structured photonic environments. Here, we introduce a constructive framework to derive quantum-optical lattice descriptions that overcome this trade-off. Combining symmetry-constrained tight-binding constructions with numerically computed photonic band structures and field profiles, our method yields minimal, symmetry-enforced lattice Hamiltonians that reproduce the target photonic dispersion while retaining the mode-resolved (position- and polarization-dependent) structure of the light-matter coupling. We show that these models recover Green's-function-based emitter dynamics in the perturbative regime, while providing access to non-perturbative quantum dynamical simulations beyond emitter-only descriptions. As a proof of principle, we apply the framework to a two-dimensional photonic crystal and show that it captures polarization-dependent directional emission inaccessible to scalar models, while enabling the analysis of non-Markovian light-matter dynamics and entanglement. Our results provide a practical bridge between classical electromagnetic simulation tools and quantum-optical many-body and non-Markovian modeling in photonic crystal settings.
Two-dimensional atomic arrays exhibit a number of intriguing quantum optical phenomena, including subradiance, nearly perfect reflection of radiation, and long-lived topological edge states. Studies of emission and scattering of photons in such lattices require complete treatment of the radiation pattern from individual atoms, including long-range interactions. We describe a systematic approach to perform the calculations of collective energy shifts and decay rates in the presence of such long-range interactions for arbitrary two-dimensional atomic lattices. As applications of our method, we investigate the topological properties of atomic lattices both in free space and near plasmonic surfaces.