莫特区域费米子异核二聚体的杰恩斯-卡明斯动力学
Jaynes--Cummings dynamics of fermionic heteronuclear dimers in the Mott regime
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中文总结 AI 辅助
该研究构建并精确求解深晶格莫特区域费米子异核二聚体的相干转换模型，将其映射为杰恩斯-卡明斯哈密顿量，推导了相关动力学的精确解析表达式，为对应物理提供了物质波实现与可解框架。
中文摘要 AI 辅助
我们构建并精确求解了深晶格莫特区域中费米子异核二聚体的相干缔合与解离模型。从格点内三组分原子-分子哈密顿量出发，我们展示了单格点模型如何映射为量子光学中的经典杰恩斯-卡明斯哈密顿量。在该映射中，费米子分子/自由原子部分构成有效二能级系统，而玻色子原子模式则扮演振子自由度的角色。我们将费米子组成原子的守恒数固定为1，同时允许玻色子组成原子的守恒数N为任意值。可及的双重态为|e,N−1⟩↔|g,N⟩，相干转换耦合被玻色子增强为χ√N。我们推导了分子解离、原子对缔合、模式布居以及玻色子-费米子关联动力学的精确解析表达式。该模型为异核玻色-费米系统中杰恩斯-卡明斯物理提供了清晰的物质波实现，并为理解晶格系统中的相干原子-分子转换及玻色子增强提供了可精确求解的框架。
英文摘要
We formulate and exactly solve a model for coherent association and dissociation of fermionic heteronuclear dimers in the deep-lattice Mott regime. Starting from the onsite three-component atom--molecule Hamiltonian, we show how the single-site model maps to the paradigmatic Jaynes--Cummings Hamiltonian from quantum optics. In this mapping, the fermionic molecular/free-atom sector forms an effective two-level system, while the bosonic atomic mode plays the role of the oscillator degree of freedom. We fix the conserved number of fermionic constituent atoms to one but allow an arbitrary conserved number $N$ of bosonic constituent atoms. The accessible doublet is then $|e,N-1\rangle\leftrightarrow|g,N\rangle$, and the coherent conversion coupling is bosonically enhanced to $χ\sqrt{N}$. Exact analytic expressions are derived for molecular dissociation, atom-pair association, mode populations, and boson--fermion correlation dynamics. The model provides a transparent matter-wave realization of Jaynes--Cummings physics in a heteronuclear Bose--Fermi system and an exactly solvable setting for understanding coherent atom--molecule conversion and bosonic enhancement in lattice systems.
