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Applied Physics Letters

Extended many-body superradiance in diamond epsilon near-zero metamaterials

Olivia Mello, Yang Li, Philip Camayd-Muñoz, Clayton DeVault, Michaël Lobet, Haoning Tang, Marko Lončar, Eric Mazur

Published Feb 7, 2022• 24 citations
Publisher

Abstract

We theoretically and numerically demonstrate enhanced extended superradiance using a diamond epsilon near-zero metamaterial design. Due to the large spatial coherence in this metamaterial, we experience an ultra-high superradiant decay rate enhancement over distances greater than 13 times the free-space wavelength for both two emitters and many-body configurations of emitters. We observe a power enhancement three orders of magnitude higher than an incoherent array of emitters in bulk diamond, corresponding to an N2 scaling with the number of emitters characteristic of superradiance.

DOI
10.1063/5.0062869

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We theoretically and numerically demonstrate enhanced extended superradiance using a diamond epsilon near-zero metamaterial design. Due to the large spatial coherence in this metamaterial, we experience an ultra-high superradiant decay rate enhancement over distances greater than 13 times the free-space wavelength for both two emitters and many-body configurations of emitters. We observe a power enhancement three orders of magnitude higher than an incoherent array of emitters in bulk diamond, corresponding to an N2 scaling with the number of emitters characteristic of superradiance.
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We develop a rigorous theory for nanophotonic cooperative spontaneous emission of an ensemble of quantum emitters near matter, which also incorporates absorption. Such theory is highly requested since one should expect that in the field of nanophotonics the close-by emitters will emit cooperatively simultaneously with strong interaction with the exotic metamaterial complex dielectric function. The closed-form model developed here considers the buildup both of interemitter correlation over time through emitter transitions via the mutual field and of geometry-induced spatial correlation. The presence of matter alters the local density of states (LDOS), resulting in modified decay rate and emission intensity for the entire ensemble relative to values of spontaneous emission in free space. The superradiant total emission is separable into a quantum-mechanical time-dependent part and a classical space-dependent part, both being functions of the LDOS. Two distinct radiative emitter--far-field coupling mechanisms, which together account for the superradiant emission, are obtained---the coupling of every individual emitter with the far field and the coupling of emitter pairs to the far field. The calculations for superradiating emitters near silver and near-zero epsilon (NZE) materials were performed with the following results: the silver sphere augments the superradiant far-field intensity and rate by up to 400 and 1000%, respectively, while the NZE sphere enhances the far-field intensity and rate of the superradiance by approximately 1400 and 400%, respectively.
Dicke superradiance is essentially a case of correlated dissipation leading to the macroscopic quantum coherence. Superradiance for arrays of inverted emitters in free space requires interactions far beyond the nearest neighbor, limiting its occurrence to small emitter-emitter distances. Epsilon-near-zero (ENZ) materials, which exhibit infinite effective wavelengths, can mediate long-range interactions between emitters. We investigate the superradiance properties of two ENZ structures, namely plasmonic waveguides and dielectric photonic crystals, and demonstrate their potential to support near-ideal Dicke superradiance across expanded spatial domains. We employ a general method that we have developed to assess the occurrence of superradiance, which is applicable to various coupling scenarios and relies only on the decoherence matrix. Furthermore, by numerically examining the emission dynamics of the few-emitter systems, we distinguish the roles of quantum coherence at different stages of emission for the case of all-to-all interaction, and demonstrate that the maximum quantum coherence in the system can be determined using the maximum photon burst rate. The findings of this work have prospective applications in quantum information processing and light-matter interaction.
An array of N closely spaced dipole coupled quantum emitters exhibits super- and subradiance with characteristic tailorable spatial radiation patterns. Optimizing the emitter geometry and distance with respect to the spatial profile of a near resonant optical cavity mode allows us to increase the ratio between light scattering into the cavity mode and free space emission by several orders of magnitude. This leads to distinct scaling of the collective coherent emitter-field coupling vs the free space decay as a function of the emitter number. In particular, for subradiant states, the effective cooperativity increases much faster than the typical linear ∝N scaling for independent emitters. This extraordinary collective enhancement is manifested both in the amplitude and the phase profile of narrow collective antiresonances appearing at the cavity output port in transmission spectroscopy.
Superradiance and subradiance are collective effects that emerge from coherent interactions between quantum emitters. Due to their many-body nature, theoretical studies of extended samples with length larger than the atomic transition wavelength are usually restricted to their early-time behavior or to the few-excitation limit. We use herein a mean-field approach to reduce the complex many-body system to an effective two-atom master equation that includes all correlations up to second order and that can be numerically propagated in time. We find that three-dimensional and two-dimensional inverted atomic arrays sustain superradiance below a critical lattice spacing and quantify the scaling of the superradiant peak for both dimensionalities. Finally, we study the late-time dynamics of the system and demonstrate that a subradiant phase appears before the system finally relaxes.