Modified<i>n</i>-level,<i>n</i>− 1-mode Tavis–Cummings model and algebraic Bethe ansatz

Skrypnyk, T.

doi:10.1088/1751-8121/aa94af

Cited by 4 publications

(1 citation statement)

References 28 publications

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“…The dynamics of the interaction between many multi-level systems and several EM modes has been discussed when non-energy-conserving terms of the Hamiltonian can be neglected, i.e., under the so-called rotating wave approximation (RWA) [32][33][34]. From these studies, it is known that analytical solutions exist for the coupling of r-level systems to r−1 EM modes [35]. In the context of the problem of N molecules coupled to a single EM mode, the RWA allows separating the Hamiltonian of the system allowing numerical approaches to the computation of exact solutions.…”

Section: Introductionmentioning

confidence: 99%

Generalization of the Tavis-Cummings model for multi-level anharmonic systems

Campos-Gonzalez-Angulo,

Ribeiro,

Yuen-Zhou

2021

Preprint

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The interaction between anharmonic quantum emitters (e.g., molecular vibrations) and confined electromagnetic fields gives rise to quantum states with optical and chemical properties that are different from those of their precursors. The exploration of these properties has been typically constrained to the first excitation manifold, the harmonic approximation, ensembles of two-level systems [Tavis-Cummings (TC) model], or the anharmonic single-molecule case. The present work studies, for the first time, a collective ensemble of identical multi-level anharmonic emitters and their dipolar interaction with a photonic cavity mode. The permutational properties of the system allow identifying symmetry classified submanifolds in the energy spectrum. Notably, in this approach, the number of particles, typically in the order of several millions, becomes only a parameter from the operational standpoint, and the size of the dimension of the matrices to diagonalize is independent of it. The formalism capabilities are illustrated by showing the energy spectrum structure, up to the third excitation manifold, and the calculation of the photon contents as a permutationally invariant quantity. Emphasis is placed on (a) the collective (superradiant) scalings of light-matter couplings and the various submanifolds of dark (subradiant) states with no counterpart in the single-molecule case, as well as (b) the delocalized modes containing more than one excitation per molecule with no equivalent in the TC model. We expect these findings to be applicable in the study of non-linear spectroscopy and chemistry of polaritons.

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Section: Introductionmentioning

confidence: 99%

Generalization of the Tavis-Cummings model for multi-level anharmonic systems

Campos-Gonzalez-Angulo,

Ribeiro,

Yuen-Zhou

2021

Preprint

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Richardson-Gaudin states

Johnson

2024

Advances in Quantum Chemistry

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Exact Solution of a Non-Hermitian Generalized Rabi Model

Cao¹,

Cao²

2021

Chinese Phys. Lett.

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An integrable non-Hermitian generalized Rabi model is constructed. A twist matrix is introduced to the construction of Hamiltonian and generates the non-Hermitian properties. The Yang-Baxter integrability of the system is proven. The exact energy spectrum and eigenstates are obtained using the Bethe ansatz. The method given in this study provides a general way to construct integrable spin-boson models.

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Modifiedn-level,n− 1-mode Tavis–Cummings model and algebraic Bethe ansatz

Cited by 4 publications

References 28 publications

Generalization of the Tavis-Cummings model for multi-level anharmonic systems

Generalization of the Tavis-Cummings model for multi-level anharmonic systems

Richardson-Gaudin states

Exact Solution of a Non-Hermitian Generalized Rabi Model

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