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arXiv:2211.13595 · Quantum

Modified dipole-dipole interactions in the presence of a nanophotonic waveguide

Mathias B. M. Svendsen, Beatriz Olmos

Published Aug 22, 2023• 5 citations
arXivHTMLPDF

Abstract

When an emitter ensemble interacts with the electromagnetic field, dipole-dipole interactions are induced between the emitters. The magnitude and shape of these interactions are fully determined by the specific form of the electromagnetic field modes. If the emitters are placed in the vicinity of a nanophotonic waveguide, such as a cylindrical nanofiber, the complex functional form of these modes makes the analytical evaluation of the dipole-dipole interaction cumbersome and numerically costly. In this work, we provide a full detailed description of how to successfully calculate these interactions, outlining a method that can be easily extended to other environments and boundary conditions. Such exact evaluation is of importance as, due to the collective character of the interactions and dissipation in this kind of systems, any small modification of the interactions may lead to dramatic changes in experimental observables, particularly as the number of emitters increases. We illustrate this by calculating the transmission signal of the light guided by a cylindrical nanofiber in the presence of a nearby chain of emitters.

DOI
10.22331/q-2023-08-22-1091

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When an emitter ensemble interacts with the electromagnetic field, dipole-dipole interactions are induced between the emitters. The magnitude and shape of these interactions are fully determined by the specific form of the electromagnetic field modes. If the emitters are placed in the vicinity of a nanophotonic waveguide, such as a cylindrical nanofiber, the complex functional form of these modes makes the analytical evaluation of the dipole-dipole interaction cumbersome and numerically costly. In this work, we provide a full detailed description of how to successfully calculate these interactions, outlining a method that can be easily extended to other environments and boundary conditions. Such exact evaluation is of importance as, due to the collective character of the interactions and dissipation in this kind of systems, any small modification of the interactions may lead to dramatic changes in experimental observables, particularly as the number of emitters increases. We illustrate this by calculating the transmission signal of the light guided by a cylindrical nanofiber in the presence of a nearby chain of emitters.
We study the interaction of emitters with a composite waveguide formed from two parallel optical nanofibers in regimes of experimental importance for atomic gases or solid-state emitters. Using the exact dyadic Green's function we comprehensively investigate the coupling efficiency and the fiber-induced Lamb shift accounting for variations in emitter positions and fiber configurations. This reveals coupling efficiencies and Purcell factors that are enhanced considerably beyond those using a single fiber waveguide, and robustness in the figures of merit. We finally investigate resonant dipole-dipole interactions and the generation of entanglement between two emitters mediated through the composite waveguide under excitation. We show that the concurrence can be enhanced for two fiber systems, such that entanglement may be present even in cases where it is zero for a single fiber. All-fiber systems are simple in construction and benefit from a wealth of existing telecommunications technologies, while enjoying strong couplings to emitters and offering interesting light-matter functionalities specific to slot waveguides. Published by the American Physical Society 2024
We study the interaction of emitters with a composite waveguide formed from two parallel optical nanofibers in currently unexplored regimes of experimental importance for atomic gases or solid-state emitters. Using the exact dyadic Green's function we comprehensively investigate the coupling efficiency and the fiber-induced Lamb shift accounting for variations in emitter positions and fiber configurations. This reveals coupling efficiencies and Purcell factors that are enhanced considerably beyond those using a single fiber waveguide, and robustness in the figures of merit. We finally investigate resonant dipole-dipole interactions and the generation of entanglement between two emitters mediated through the composite waveguide under excitation. We show that the concurrence can be enhanced for two fiber systems, such that entanglement may be present even in cases where it is zero for a single fiber. All-fiber systems are simple in construction and benefit from a wealth of existing telecommunications technologies, whilst enjoying strong couplings to emitters and offering novel light-matter functionalities specific to slot waveguides.
We investigate the radiative coupling between two two-level atoms with arbitrarily polarized dipoles in the vicinity of a nanofiber. We present a systematic derivation for the master equation, the single- and cross-atom decay coefficients, and the dipole-dipole interaction coefficients for the atoms interacting with the vacuum of the field in the guided and radiation modes of the nanofiber. We study numerically the case where the atomic dipoles are circularly polarized. In this case, the rate of emission depends on the propagation direction, that is, the radiative interaction between the atoms is chiral. We examine the time evolution of the atoms for different initial states. We calculate the fluxes and mean numbers of photons spontaneously emitted into guided modes in the positive and negative directions of the fiber axis. We show that the chiral radiative coupling modifies the collective emission of the atoms. We observe that the modifications strongly depend on the initial state of the atomic system, the radiative transfer direction, the distance between the atoms, and the distance from the atoms to the fiber surface.
We investigate the radiative coupling between two two-level atoms with arbitrarily polarized dipoles in the vicinity of a nanofiber. We present a systematic derivation for the master equation, the single- and cross-atom decay coefficients, and the dipole-dipole interaction coefficients for the atoms interacting with the vacuum of the field in the guided and radiation modes of the nanofiber. We study numerically the case where the atomic dipoles are circularly polarized. In this case, the rate of emission depends on the propagation direction along the fiber axis and, hence, the radiative interaction between the atoms is chiral. We examine the time evolution of the atoms for different initial states. We calculate the fluxes and mean numbers of photons spontaneously emitted into guided modes in the positive and negative directions of the fiber axis. We show that the chiral radiative coupling modifies the collective emission of the atoms. We observe that the modifications strongly depend on the initial state of the atomic system, the radiative transfer direction, the distance between the atoms, and the distance from the atoms to the fiber surface.
Several methods have been developed to calculate the spontaneous emission rate for extended emitters in the vicinity of a nanophotonic structure.While taking the emitter's spatial extension, these methods have taken approximations regarding the full interaction, either by coupling to one single plasmonic mode or adding higher order rates individually thus neglecting interference terms.Here we apply a new framework [1] to extended emitters, by which, all these interactions can be considered, and we show both under, and over-estimation of the Purcell Factor when using a point-dipole.