The $k$-photon quantum Rabi model
- URL: http://arxiv.org/abs/2401.02370v1
- Date: Thu, 4 Jan 2024 17:25:50 GMT
- Title: The $k$-photon quantum Rabi model
- Authors: Daniel Braak
- Abstract summary: A generalization of the quantum Rabi model is obtained by replacing the linear (dipole) coupling between the two-level system and the radiation mode.
If each spin flip involves $k$ photons, it is called the "$k$-photon" quantum Rabi model.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: 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.
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