arXiv 2409.045552024-09-06quant-ph

存在 $A^{2}$ 项时 Rabi 模型中的量子纠缠

Quantum Entanglement in the Rabi Model with the Presence of the $A^{2}$ Term

Zakaria Boutakka, Zoubida Sakhi, Mohamed Bennai

AI总结：

该研究比较含与不含 $A^{2}$ 项的量子 Rabi 模型，结合能谱、Wigner 函数和 Von Neumann 熵分析强耦合基态，证明 $A^{2}$ 项与 Fock 态数显著影响量子纠缠。

摘要：

量子 Rabi 模型（QRM）用于描述腔量子电动力学（Cavity QED）中量子层面的光与物质相互作用。它由与单模量子场耦合的二能级系统（原子或量子比特）组成，而将原子引入腔中会改变腔内的电磁模式构型。在 Cavity QED 领域，这种改变的一个显著结果是出现了依赖规范的抗磁项，称为 $A^{2}$ 贡献。在本研究中，我们通过考察强耦合区的能谱性质，比较分析了 QRM 的行为以及 $A^{2}$ 项在光-物质量子哈密顿量中的影响。随后，我们研究系统的基态，针对 Fock 空间中不同的光子数分布，通过 Wigner 分布函数测量其非经典性质。最后，我们通过 Von Neumann 熵计算基态中的量子纠缠。研究结果表明，$A^{2}$ 项和腔 Fock 态数 $N$ 显著影响量子纠缠的大小，凸显了它们的关键作用。

英文摘要：

The quantum Rabi model (QRM) is used to describe the light-matter interaction at the quantum level in Cavity Quantum Electrodynamics (Cavity QED). It consists of a two-level system (atom or qubit) coupled to a single-mode quantum field, and by introducing an atom into a cavity alters the electromagnetic mode configuration within it. In the realm of Cavity QED, a notable consequence of this alteration is the emergence of a gauge-dependent diamagnetic term referred to as the $A^{2}$ contribution. In this study, we comparatively analyze the behaviors of the QRM and the influence of the $A^{2}$ term in the light-matter quantum Hamiltonian by examining the energy spectrum properties in the strong-coupling regime. We then investigate the ground state of the system, measuring its nonclassical properties via the Wigner distribution function for different photon number distribution in Fock space. Finally, we calculate the quantum entanglement in the ground state over the Von Neumann entropy. Our findings reveal that the $A^{2}$ term and the number of cavity Fock states $N$ significantly impact the amount of the quantum entanglement, highlighting their pivotal role.

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