The $k$-photon quantum Rabi model
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910865546018816 |
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| author | Braak, Daniel |
| author_facet | Braak, Daniel |
| contents | A generalization of the quantum Rabi model is obtained by replacing the linear (dipole) coupling between the two-level system and the radiation mode by a non-linear expression in the creation and annihilation operators, corresponding to multi-photon excitations. If each spin flip involves $k$ photons, it is called the "$k$-photon" quantum Rabi model. While the formally symmetric Hamilton operator is self-adjoint in the case $k=2$, it is demonstrated here that the Hamiltonian is not self-adjoint for $k\ge 3$. Therefore it does not generate a unitary time evolution and is unphysical. This result cannot be obtained by numerical calculations in finite-dimensional spaces which attempt to approximate an unbounded operator by a finite-rank operator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_02370 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The $k$-photon quantum Rabi model Braak, Daniel Quantum Physics Mathematical Physics A generalization of the quantum Rabi model is obtained by replacing the linear (dipole) coupling between the two-level system and the radiation mode by a non-linear expression in the creation and annihilation operators, corresponding to multi-photon excitations. If each spin flip involves $k$ photons, it is called the "$k$-photon" quantum Rabi model. While the formally symmetric Hamilton operator is self-adjoint in the case $k=2$, it is demonstrated here that the Hamiltonian is not self-adjoint for $k\ge 3$. Therefore it does not generate a unitary time evolution and is unphysical. This result cannot be obtained by numerical calculations in finite-dimensional spaces which attempt to approximate an unbounded operator by a finite-rank operator. |
| title | The $k$-photon quantum Rabi model |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2401.02370 |