Engineering Photon-mediated Long-Range Spin Interactions in Mott Insulators
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| Format: | Preprint |
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2023
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| author | Fadler, Paul Li, Jiajun Schmidt, Kai Phillip Eckstein, Martin |
| author_facet | Fadler, Paul Li, Jiajun Schmidt, Kai Phillip Eckstein, Martin |
| contents | We investigate the potential to induce long-range spin interactions in a Mott insulator via the quantum electromagnetic field of a cavity. The coupling between light and spins is inherently non-linear, and occurs via multi-photon processes like Raman scattering and two-photon absorption/emission with electronically excited intermediate states. Based on this, two pathways are elucidated: (i) In the absence of external driving, long-range interactions are mediated by the exchange of at least two virtual cavity photons. We show that these vacuum-mediated interactions can surpass local Heisenberg interactions in mesoscopic setups such as sufficiently small split-ring resonators. (ii) In a laser-driven cavity, interactions can be tailored through a hybrid scheme involving both external laser photons and cavity photons. This offers a versatile pathway for Floquet engineering of long-range interactions in macroscopic systems. In general, the derivation of these interactions requires careful consideration: Notably, we demonstrate that a simple phenomenological approach, based on a spin-photon Hamiltonian that captures Raman and two-photon processes with effective matrix elements, can be used only if the cavity is resonantly driven. Outside of these narrow resonant regimes as well as for the undriven case, a fourth-order series expansion within the underlying electronic model is necessary, which we perform to obtain long-range four-spin interactions in the half-filled Hubbard model. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2311_01339 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Engineering Photon-mediated Long-Range Spin Interactions in Mott Insulators Fadler, Paul Li, Jiajun Schmidt, Kai Phillip Eckstein, Martin Strongly Correlated Electrons Mesoscale and Nanoscale Physics We investigate the potential to induce long-range spin interactions in a Mott insulator via the quantum electromagnetic field of a cavity. The coupling between light and spins is inherently non-linear, and occurs via multi-photon processes like Raman scattering and two-photon absorption/emission with electronically excited intermediate states. Based on this, two pathways are elucidated: (i) In the absence of external driving, long-range interactions are mediated by the exchange of at least two virtual cavity photons. We show that these vacuum-mediated interactions can surpass local Heisenberg interactions in mesoscopic setups such as sufficiently small split-ring resonators. (ii) In a laser-driven cavity, interactions can be tailored through a hybrid scheme involving both external laser photons and cavity photons. This offers a versatile pathway for Floquet engineering of long-range interactions in macroscopic systems. In general, the derivation of these interactions requires careful consideration: Notably, we demonstrate that a simple phenomenological approach, based on a spin-photon Hamiltonian that captures Raman and two-photon processes with effective matrix elements, can be used only if the cavity is resonantly driven. Outside of these narrow resonant regimes as well as for the undriven case, a fourth-order series expansion within the underlying electronic model is necessary, which we perform to obtain long-range four-spin interactions in the half-filled Hubbard model. |
| title | Engineering Photon-mediated Long-Range Spin Interactions in Mott Insulators |
| topic | Strongly Correlated Electrons Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2311.01339 |