论文标题
使用$ \ boldsymbol {\ mathsf {a}}}^{2} $ term the量子拉比模型的精确解决方案
Exact solution for the quantum Rabi model with the $\boldsymbol{\mathsf{A}}^{2}$ term
论文作者
论文摘要
量子性兔模型（QRM）广泛用于分析腔量子电动力学基本水平的辐射 - 物质相互作用。通常，QRM Hamiltonian仅包含$ \ boldsymbol {\ MathSf {p}} \ cdot \ boldsymbol {\ Mathsf {a}} $ enmer，但是，完全非递归的量子量化量子动力学的量子量} =} $ at} $ n} $ n} $ n} =在这里，我们找到了一个精确的解决方案，并在确切的规范转换的帮助下证明了QRM Hamiltonian，其$ \ boldsymbol {\ MathSf {\ MathSf {a}}^{2} $ term（qRMA）被简化为标准的QRM Hamiltonian，并通过恢复的频率和脉冲状态，并通过COUTEED和EDECEED squedeed squper squper squper and couplate squeed squeed squeed squeed squeed squeed squeed squeed squeed squeed sque egi egiemenStates is eigieMenStates。结果，$ \ boldsymbol {\ mathsf {a}}^{2} $术语在质量上改变了QRM的行为，其在强耦合方面纯粹是电磁相互作用的行为：在坚固的耦合方面：在空腔内部原子的基态能量的值高于真空的数量和不同数量的交叉数量。
Quantum Rabi model (QRM) is widely used for the analysis of the radiation-matter interaction at the fundamental level in cavity quantum electrodynamics. Typically the QRM Hamiltonian includes only $\boldsymbol{\mathsf{p}} \cdot \boldsymbol{\mathsf{A}}$ term, however, the complete nonrelativistic Hamiltonian of quantum electrodynamics includes $\boldsymbol{\mathsf{A}}^{2}$ term as well. Here we find an exact solution and demonstrate with the help of the exact canonical transformations that the QRM Hamiltonian with the $\boldsymbol{\mathsf{A}}^{2}$ term (QRMA) is reduced to the standard QRM model Hamiltonian with the renormalized frequency and the coupling constant and the eigenstates are expressed through the squeezed states of the field. As a result, the $\boldsymbol{\mathsf{A}}^{2}$ term qualitatively changes the behavior of the QRM with purely electromagnetic interaction in the strong coupling regime: the value of the ground state energy of an atom inside the cavity is higher than in vacuum and the number of crossing of energy levels with different quantum numbers decreases.
