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Physical Review Letters

Quantum Nonreciprocity of Nanoscale Antenna Arrays in Timed Dicke States

Gregory Ya. Slepyan, Amir Boag

Published Jul 11, 2013• 49 citations
Publisher

Abstract

We predict a linear nonreciprocal effect that is based on the timed Dicke states in an ensemble of dipole-dipole coupled oscillators. This effect is examined on a nanoscale antenna array comprising two-level identical emitters. The studied nonreciprocity, which has no analogs in classical antennas, manifests itself in strong characteristic asymmetry of the radiation pattern, even for a single-photon laser pumping. Promising applications of our results for remotely tunable nanoantennas and nanocircuit elements are discussed.

DOI
10.1103/physrevlett.111.023602

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We predict a linear nonreciprocal effect that is based on the timed Dicke states in an ensemble of dipole-dipole coupled oscillators. This effect is examined on a nanoscale antenna array comprising two-level identical emitters. The studied nonreciprocity, which has no analogs in classical antennas, manifests itself in strong characteristic asymmetry of the radiation pattern, even for a single-photon laser pumping. Promising applications of our results for remotely tunable nanoantennas and nanocircuit elements are discussed.
A quantum-dot array prepared in a timed Dicke state exhibits directional radiation asymmetry, which has often been interpreted as evidence of reciprocity breaking through quantum-state preparation. We show that this interpretation is incorrect: reciprocity concerns transmit-receive response, not necessarily pattern symmetry. Moreover, the first-order coherence of any single-excitation state is exactly equivalent to the power pattern of a classical phased array driven by conjugate weights, making the observed asymmetry classically reproducible. The genuine quantum signature instead appears in second-order correlations, where a single-excitation state violates the classical lower bound on photon coincidences. We therefore propose a quantum-antenna certificate combining nonzero directional asymmetry with photon antibunching at the beam peak. We further derive a tight asymmetry bound, establish the correct mirror operation for planar arrays, correct the collective decay rate with dipole-dipole coupling, and derive a saturation law for direction-finding precision. All theoretical results are validated through independent numerical implementations.
We investigate the collective spontaneous emission in a system of two identical quantum dots (QDs) strongly coupled through the dipole-dipole ($d\ensuremath{-}d$) interaction. The QDs are modeled as two-level quantum objects, while the $d\ensuremath{-}d$ interaction is described as the exchange of a virtual photon through the photonic reservoir. The master equation approach is used in the analysis. The main attention is focused on antenna characteristics of the two-QD system---the radiation intensity dependence on the meridian and azimuthal angles of observation. We show that the radiation pattern of such a system is nonstationary and its temporal behavior depends on the initial quantum state. In particular, for entangled initial states the radiative pattern exhibits oscillations on the frequency which corresponds to the $d\ensuremath{-}d$ interaction energy. We also analyze spectral properties of the directional diagram. The comparison of radiation patterns is carried out for two QDs and two classical dipoles. The concept of quantum nanoantenna is proposed based on collective spontaneous emission in QD ensembles.
Cavity quantum electrodynamics is the art of enhancing light-matter interaction of photon emitters in cavities with opportunities for sensing, quantum information, and energy capture technologies. To boost emitter-cavity interaction, that is, coupling strength g, ultrahigh quality cavities have been concocted yielding photon trapping times of microsecondsy to milliseconds. However, such high- Q cavities give poor photon output, hindering applications. To preserve high photon output, it is advantageous to strive for highly localized electric fields in radiatively lossy cavities. Nanophotonic antennas are ideal candidates combining low- Q factors with deeply localized mode volumes, allowing large g, provided the emitter is positioned exactly right inside the nanoscale mode volume. Here, with nanometer resolution, we map and tune the coupling strength between a dipole nanoantenna-cavity and a single molecule, obtaining a coupling rate of g max ∼ 200 GHz. Together with accelerated single photon output, this provides ideal conditions for fast and pure nonclassical single photon emission with brightness exceeding 10 9 photons/sec. Clearly, nanoantennas acting as “bad” cavities offer an optimal regime for strong coupling g to deliver bright on-demand and ultrafast single photon nanosources for quantum technologies.
Subwavelength arrays of quantum emitters feature unique and largely design-able nonlinear optical properties. As a generic example we study a sub-wavelength sized ring of identical dipoles with an extra identical absorbing emitter at the center. For a 9-ring one finds the most efficient antenna configuration to direct single incoming photons to the center without re-emission. Interestingly, for very tiny structures sizes below a tenth of a wavelength, a full quantum description predicts an even larger absorption enhancement than a mean field model using a classical dipole approximation. We identify the origin of the enhancement in the appearance of a collective dark state with dominant center occupation. By special design of the center absorber one thus can harness the same efficiency enhancement also at different wavelengths and for other geometric structures. On the one hand this idea could be the basis of a new generation of highly efficient and selective nano antennas, while on the other hand, it could be an important piece towards understanding the surprising efficiency of natural light harvesting molecules. Adding gain via active dipoles in such nano ring systems allows to design minimalist laser like classical light sources. In the nonlinear operating regime at stronger pump fields these systems transform to non-classical light sources with tailor-able spatio-temporal emission upon coherent illumination.
Regular arrays of two-level emitters at distances smaller than that of the transition wavelength collectively scatter, absorb, and emit photons. The strong inter-particle dipole coupling creates large energy shifts of the collective delocalized excitations, which generates a highly nonlinear response at the single and few photon level. This should allow us to implement nanoscale non-classical light sources via weak coherent illumination. At the generic tailored examples of regular chains or polygons, we show that the fields emitted perpendicular to the illumination direction exhibit a strong directional confinement with genuine quantum properties as antibunching. For short interparticle distances, superradiant directional emission can enhance the radiated intensity by an order of magnitude compared to a single atom focused to a strongly confined solid angle but still keeping the anti-bunching parameter at the level of g(2)(0)≈10−2.
We investigate the role of quantum interference phenomena on the characteristics of the fields radiated by an array of quantum emitters. In analogy to, but distinct from, classical outcomes, we demonstrate that the array geometry empowers control over direction-dependent photon statistics of arbitrary order. Our formulation enables the recognition of configurations providing spatial correlations with no classical counterpart. For example, we identify a system in which the angular distribution of the average number of photons is independent of the number and position of the emitters, while its higher-order photon statistics exhibit a directional behavior. These results extend our understanding of the fields generated by ensembles of quantum emitters, with potential applications to nonclassical light sources.