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Bulletin of the American Physical Society

Light-matter interactions in optical cavities beyond the classical Maxwell description

Norah M. Hoffmann, Aaron Kelly, Niko Säkkinen, Christian Schaefer, Ángel Rubio, Neepa T. Maitra, Heiko Appel

Published Mar 5, 2018• 0 citations
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Floquet physics from quantized light-matter interaction: geometric phases, gauge consistency, and entanglement

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Floquet engineering and cavity quantum electrodynamics represent two complementary descriptions of light-matter interaction, yet their precise connection beyond the small-coupling regime remains subtle. Here, by representing the cavity field in a large-photon-number phase basis, we show that the time-dependent Schrödinger equation of a classically driven system emerges directly from the fully quantized problem, without replacing the field by a classical trajectory or assuming a mean-field decoupling. This establishes a one-to-one correspondence between quasienergies and photon-sector-shifted quantum energies, while providing a direct quantum interpretation of the Floquet mean energy and Anandan phase. Because gauge invariance is exactly preserved at the level of the quantum Hamiltonian, the quantum-to-classical correspondence remains valid beyond perturbative and small-coupling regimes. We further show that light--matter entanglement is encoded in matter--harmonic correlations of the corresponding Floquet mode, thus identifying a semiclassical limit in which Floquet physics emerges without requiring the quantum field itself to approach a coherent classical state.

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Attempting to implement quantum information related applications utilizing atoms and photons, as they naturally form quantum systems supporting superposition states, hybrid quantum plasmonic systems emerged in the past as a platform to study and engineer light-matter interaction. This platform combines the unrivaled electromagnetic field localization of surface plasmon polaritons, boosting the light-matter coupling rate, with the tremendous integration potential of truly nanoscale structures, and both the significant emission rates of nanoantennas and photonic transmission velocities. In this work, a classical description of surface plasmon polaritons is combined with a light-matter interaction model based on a cavity quantum electrodynamical formalism. The resulting composite semi-classical method, introduced and described in this thesis, provides efficient and versatile means to simulate the dynamical behavior of radiative atomic transitions coupled to plasmonic cavity modes in the weak incoherent coupling regime. Both the emission into the far field and various dissipation mechanisms are included by expanding the model to an open quantum system. The variety of light-matter interaction applications that can be modeled with the outlined method is indicated by the four different exemplary scenarios detailed in the application chapter of this thesis. The classical description of localized surface plasmon polaritons is benchmarked by reproducing the experimental measurements of the molecular fluorescence manipulation through optical nanoantennas in a collaborative effort with experimental partners. Furthermore, in the weak light-matter coupling regime, the potential of achieving a higher nanoantenna functionality and simultaneously realizing more elaborate quantum dynamics is revealed by the three remaining applications. Each pivotally involving a bimodal nanoantenna and demonstrating different quantum optical phenomena, the implementation of cavity radiation mode conversion, non-classical cavity emission statistics, and non-classical cavity emission properties is shown and described in the application chapter.

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Constructing mode-resolved quantum optical models for emitters in photonic crystals

Antonio Morales-Pérez, Iñaki García-Elcano, Chiara Devescovi +3 more

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.

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Correlated Light-Matter Interactions in Picocavities and Cavity QED

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Bulletin of the American Physical Society•Mar 8, 2018•0 citations
Floquet engineering and cavity quantum electrodynamics represent two complementary descriptions of light-matter interaction, yet their precise connection beyond the small-coupling regime remains subtle. Here, by representing the cavity field in a large-photon-number phase basis, we show that the time-dependent Schrödinger equation of a classically driven system emerges directly from the fully quantized problem, without replacing the field by a classical trajectory or assuming a mean-field decoupling. This establishes a one-to-one correspondence between quasienergies and photon-sector-shifted quantum energies, while providing a direct quantum interpretation of the Floquet mean energy and Anandan phase. Because gauge invariance is exactly preserved at the level of the quantum Hamiltonian, the quantum-to-classical correspondence remains valid beyond perturbative and small-coupling regimes. We further show that light--matter entanglement is encoded in matter--harmonic correlations of the corresponding Floquet mode, thus identifying a semiclassical limit in which Floquet physics emerges without requiring the quantum field itself to approach a coherent classical state.
Attempting to implement quantum information related applications utilizing atoms and photons, as they naturally form quantum systems supporting superposition states, hybrid quantum plasmonic systems emerged in the past as a platform to study and engineer light-matter interaction. This platform combines the unrivaled electromagnetic field localization of surface plasmon polaritons, boosting the light-matter coupling rate, with the tremendous integration potential of truly nanoscale structures, and both the significant emission rates of nanoantennas and photonic transmission velocities. In this work, a classical description of surface plasmon polaritons is combined with a light-matter interaction model based on a cavity quantum electrodynamical formalism. The resulting composite semi-classical method, introduced and described in this thesis, provides efficient and versatile means to simulate the dynamical behavior of radiative atomic transitions coupled to plasmonic cavity modes in the weak incoherent coupling regime. Both the emission into the far field and various dissipation mechanisms are included by expanding the model to an open quantum system. The variety of light-matter interaction applications that can be modeled with the outlined method is indicated by the four different exemplary scenarios detailed in the application chapter of this thesis. The classical description of localized surface plasmon polaritons is benchmarked by reproducing the experimental measurements of the molecular fluorescence manipulation through optical nanoantennas in a collaborative effort with experimental partners. Furthermore, in the weak light-matter coupling regime, the potential of achieving a higher nanoantenna functionality and simultaneously realizing more elaborate quantum dynamics is revealed by the three remaining applications. Each pivotally involving a bimodal nanoantenna and demonstrating different quantum optical phenomena, the implementation of cavity radiation mode conversion, non-classical cavity emission statistics, and non-classical cavity emission properties is shown and described in the application chapter.
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.