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Models of Quantum MatterA First Course on Integrability and the Bethe Ansatz$
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Hans-Peter Eckle

Print publication date: 2019

Print ISBN-13: 9780199678839

Published to Oxford Scholarship Online: September 2019

DOI: 10.1093/oso/9780199678839.001.0001

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Quantum Tavis–Cummings Model

Quantum Tavis–Cummings Model

(p.474) 12 Quantum Tavis–Cummings Model
Models of Quantum Matter

Hans-Peter Eckle

Oxford University Press

This chapter extends the algebraic Bethe ansatz to the quantum Tavis–Cummings model, an N atom generalization of the Jaynes–Cummings model to describe the strong interaction between light and quantum matter. In the case of the quantum Tavis–Cum- mings model there is no underlying vertex model to suggest the constituent building blocks of the algebraic Bethe ansatz approach, e.g.like the L-matrix or ultimately the transfer matrix. The algebraic Bethe ansatz is then first applied to the Tavis–Cummings Hamiltonian with an added Stark term using a conjecture for the transfer matrix. The original Tavis–Cummings model and its algebraic Bethe ansatz are obtained in the limit of vanishing Stark term, which requires considerable care.

Keywords:   quantum Tavis–Cummings model, Stark term, algebraic Bethe ansatz, transfer matrix, commutativity

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