Dicke model of open-shell atoms with tensor polarizability

Abstract

We study the extended Dicke model obtained from the scalar--vector--tensor polarizability of open-shell atoms coupled to a shared cavity mode. For a single electric-dipole channel, rotational symmetry fixes the tensor to vector ratio; we use ¹⁶⁸Er with J=6 as a product-state example. A circular pump produces a chiral Raman vertex whose tensor-dependent matrix elements select the occupied Zeeman sector. The resulting first-order transition occurs before the empty-cavity branch loses local stability, and the ordered state is read out through ⟨Ĵ_z⟩. A linear pump instead produces an empty-cavity ± x cat and a continuous transition into an even-m cat-like state with order parameter ⟨Ĵ_z²⟩. With cavity loss alone, the circular trajectory emits a photon burst and approaches a Raman-dark Zeeman pole rather than a finite-field condensate. In the linear geometry, cavity-bright modes are damped toward the cat-like branch while a dark spin mode remains undamped. These are phenomena of that model; the vector-only controls show that they depend on the channel-fixed tensor coupling.

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BibTeX RIS

BibTeX

@misc{zhu2026dicke,
  title = {{Dicke model of open-shell atoms with tensor polarizability}},
  author = {Ziheng Zhu and Yu Chen},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.20043},
  eprint = {2610.20043},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.20043},
}

RIS

TY  - UNPB
TI  - Dicke model of open-shell atoms with tensor polarizability
AU  - Ziheng Zhu
AU  - Yu Chen
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2610.20043
UR  - https://arxiv.org/abs/2610.20043
AB  - We study the extended Dicke model obtained from the scalar--vector--tensor polarizability of open-shell atoms coupled to a shared cavity mode. For a single electric-dipole channel, rotational symmetry fixes the tensor to vector ratio; we use ^168Er with J=6 as a product-state example. A circular pump produces a chiral Raman vertex whose tensor-dependent matrix elements select the occupied Zeeman sector. The resulting first-order transition occurs before the empty-cavity branch loses local stability, and the ordered state is read out through ⟨Ĵ_z⟩. A linear pump instead produces an empty-cavity ± x cat and a continuous transition into an even-m cat-like state with order parameter ⟨Ĵ_z^2⟩. With cavity loss alone, the circular trajectory emits a photon burst and approaches a Raman-dark Zeeman pole rather than a finite-field condensate. In the linear geometry, cavity-bright modes are damped toward the cat-like branch while a dark spin mode remains undamped. These are phenomena of that model; the vector-only controls show that they depend on the channel-fixed tensor coupling.
ER  -

Abstract

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