Emergence of fermion-mediated interactions in Bose-Fermi mixtures
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909942199353344 |
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| author | Cárdenas, Esteban Miller, Joseph K. Mitrouskas, David Pavlović, Nataša |
| author_facet | Cárdenas, Esteban Miller, Joseph K. Mitrouskas, David Pavlović, Nataša |
| contents | This work is inspired by recent experimental observations in ultracold atomic Bose-Fermi mixtures [DeSalvo et al., Nature 568 (2019)]. These experiments reveal the emergence of an attractive fermion-mediated interaction between bosons, as well as a stability-instability transition. We give the first mathematical demonstration of this transition by studying the low-energy spectrum of a many-body interspecies Hamiltonian. More precisely, we show the convergence of its eigenvalues towards those of an effective Bose Hamiltonian, which includes fermion-mediated effects. Applying this result to a model with short-range potentials, we derive a stability-instability transition in the bosonic subsystem, driven by the Bose-Fermi coupling strength $g$. For small $|g|$, the bosons form a stable Bose-Einstein condensate with the energy per particle uniformly bounded from below. For large $|g|$, the energy per particle is no longer uniformly bounded from below, signaling the collapse of the condensate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_18678 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Emergence of fermion-mediated interactions in Bose-Fermi mixtures Cárdenas, Esteban Miller, Joseph K. Mitrouskas, David Pavlović, Nataša Mathematical Physics Analysis of PDEs This work is inspired by recent experimental observations in ultracold atomic Bose-Fermi mixtures [DeSalvo et al., Nature 568 (2019)]. These experiments reveal the emergence of an attractive fermion-mediated interaction between bosons, as well as a stability-instability transition. We give the first mathematical demonstration of this transition by studying the low-energy spectrum of a many-body interspecies Hamiltonian. More precisely, we show the convergence of its eigenvalues towards those of an effective Bose Hamiltonian, which includes fermion-mediated effects. Applying this result to a model with short-range potentials, we derive a stability-instability transition in the bosonic subsystem, driven by the Bose-Fermi coupling strength $g$. For small $|g|$, the bosons form a stable Bose-Einstein condensate with the energy per particle uniformly bounded from below. For large $|g|$, the energy per particle is no longer uniformly bounded from below, signaling the collapse of the condensate. |
| title | Emergence of fermion-mediated interactions in Bose-Fermi mixtures |
| topic | Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2502.18678 |