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理论物理通讯：英文版

Exact Solution for Jaynes-Cummings Model with Bosonic Field Nonlinearity and Strong Boson-Fermion Coupling

Yang, Jin, Yu, Wan-Lun, Xiang, Anping

Published Jan 1, 2006• 2 citations
OpenAlex

Abstract

当 strongboson 费米子政变石楠是珍视的无有势力 Grassmann 时，我们使用对待 modifiedJaynes-Cummings 的不变的途径建模包含 bosonic 域的 nonlinearty 的任何表格的 Lewis-Riesenfeld。为 bosonic 号码和 fermionic 号码的一般州的函数，时间进化操作符和时间进化表达式被介绍。

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We start from a Hamiltonian describing non-interacting fermions and add bosons to the model, with a Jaynes-Cummings-like interaction between the bosons and fermions. Because of the specific form of the interaction the model can be solved exactly. In the ground state, part of the electrons form bound pairs with opposite momentum and spin. The model also shows a gap in the kinetic energy of the fermions, but not in the spectrum of the full Hamiltonian. This gap is not of a mean-field nature, but is due to the Pauli exclusion principle.
In this article we present a simple and unified procedure to solve various nonlinear two-level Jaynes-Cummings models. By establishing their similarity to the model describing a spin- particle in a magnetic field, we obtain the standardized forms, appropriate uniformly for all Jaynes-Cummings models, of eigenvalues, eigenstates, evolution, and atomic inversion operators. In this way, we show that the analytical solution of any single-mode and two-mode nonlinear Jaynes-Cummings model can easily be obtained. We also apply this procedure to a three-mode Jaynes-Cummings model.