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arXiv:2003.07854 · Physical Review A

Limits of photon-mediated interactions in one-dimensional photonic baths

Eduardo Sánchez-Burillo, Diego Porras, Alejandro González-Tudela

Published Jul 8, 2020• 16 citations
arXivHTMLPDF

Abstract

The exchange of off-resonant propagating photons between distant quantum emitters induces coherent interactions among them. The range of such interactions, and whether they are accompanied by dissipation, depends on the photonic energy dispersion, its dimensionality, and/or the light-matter couplings. We characterize the limits of photon-mediated interactions for the case of generic one-dimensional photonic baths under the typical assumptions, i.e., finite range hoppings for the photonic bath plus local and rotating-wave light-matter couplings. In that case, we show how, irrespective of the system's parameter, the coherent photon-mediated interactions can always be written as a finite sum of exponentials and thus cannot display a power-law asymptotic scaling. As an outlook, we show how by relaxing some of these conditions, e.g., going beyond local light-matter couplings (e.g., giant atoms) or with longer-range photon hopping models, power-law interactions can be obtained within certain distance windows or even in the asymptotic regime for the latter case.

DOI
10.1103/physreva.102.013709

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The exchange of off-resonant propagating photons between distant quantum emitters induces coherent interactions among them. The range of such interactions, and whether they are accompanied by dissipation, depends on the photonic energy dispersion, its dimensionality, and/or the light-matter couplings. We characterize the limits of photon-mediated interactions for the case of generic one-dimensional photonic baths under the typical assumptions, i.e., finite range hoppings for the photonic bath plus local and rotating-wave light-matter couplings. In that case, we show how, irrespective of the system's parameter, the coherent photon-mediated interactions can always be written as a finite sum of exponentials and thus cannot display a power-law asymptotic scaling. As an outlook, we show how by relaxing some of these conditions, e.g., going beyond local light-matter couplings (e.g., giant atoms) or with longer-range photon hopping models, power-law interactions can be obtained within certain distance windows or even in the asymptotic regime for the latter case.
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.
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.
We investigate the interactions between two-level emitters mediated by time-dependent, one-dimensional, structured photonic baths, focusing on Floquet topological lattices. Building on the framework of periodically driven photonic lattices, we demonstrate and characterize the emergence of tunable-range emitter interactions mediated by bound states absent in static photonic lattices. In particular, we show that one can obtain different spatial interaction dependencies not only with respect to the static bath scenarios, but also in qualitatively different regimes due to the time-dependent nature of the bath, for example, when the emitters have different frequencies. This work sheds light on the interplay between nonequilibrium photonics and quantum optics and can serve as a basis for analyzing Floquet photonic lattices in higher dimensions.
In recent years, Born-Markov master equations based on tracing out the electromagnetic degrees of freedom have been extensively employed in the description of quantum optical phenomena originating from photon-mediated interactions in quantum emitter ensembles. The breakdown of these effective models, built upon assumptions such as ensemble spectral homogeneity, an unstructured photonic density of states, and weak light-matter coupling, has also recently attracted considerable attention. Here, we investigate the accuracy of this well-established framework beyond the most conventional, and extensively explored, spontaneous emission configuration. Specifically, we consider a system comprising two coherently driven and detuned quantum emitters, embedded within a hybrid photonic-plasmonic cavity, formed by a metallic nanorod integrated into a high-refractive-index dielectric microresonator. The local density of photonic states in this structure exhibits a complex frequency dependence, making it a compelling platform for exploring photon-mediated interactions beyond the assumptions above. We benchmark this modeling approach for the quantum dynamics of the emitter pair against exact calculations based on a macroscopic field quantization formalism, providing an illustrative assessment of its validity in significantly structured and dispersive photonic environments. Our analysis reveals four distinct regimes of laser driving and frequency splitting that lead to markedly different levels of accuracy in the effective model.
Photon-mediated interaction between quantum emitters in engineered photonic baths is an emerging area of quantum optics. At the same time, non-Hermitian (NH) physics is currently thriving, spurred by the exciting possibility to access new physics in systems ruled by non-trivial NH Hamiltonians—in particular, photonic lattices—which can challenge longstanding tenets such as the Bloch theory of bands. Here, we combine these two fields and study the exotic interaction between emitters mediated by the photonic modes of a lossy photonic lattice described by a NH Hamiltonian. We show in a paradigmatic case study that structured losses in the field can seed exotic emission properties. Photons can mediate dissipative, fully non-reciprocal interactions between emitters with range critically dependent on the loss rate. When this loss rate corresponds to a bare-lattice exceptional point, the effective couplings are exactly nearest neighbor, implementing a dissipative, fully non-reciprocal Hatano–Nelson model. Counterintuitively, this can occur irrespective of the lattice boundary conditions. Thus photons can mediate an effective emitter’s Hamiltonian which is translationally invariant despite the fact that the field is not. We interpret these effects in terms of metastable atom–photon dressed states, which can be exactly localized on only two lattice cells or extended across the entire lattice. These findings introduce a paradigm of light-mediated interactions with unprecedented features such as non-reciprocity, non-trivial dependence on field boundary conditions, and range tunability via a loss rate.