论文标题
与时间相关的复杂频率之间的纠缠模式之间的纠缠
Entanglement between uncoupled modes with time-dependent complex frequencies
论文作者
论文摘要
在这项工作中，我们介绍了由时间依赖的非汉密尔顿人产生的统一时间进化的一般统一描述，这些统一的汉密尔顿人嵌入了$ \ mathfrak {sufrak {su}（1,1）$和$ \ mathfrak {sufrak {su}（su}（2）$ lie lie Algebras。我们考虑了根据这些代数的要素所写的时间依赖性的Hermitian dyson地图，该代数与非赫米特人与其Hermitian对应物之间的关系独立于代数实现。作为直接结果，我们验证，即使不存在典型的模式相互作用的交叉操作器，也可能表现出由时间依赖的复合频率调制的未耦合模式的时间进化状态。这是由于在一般Hermitian Dyson地图的时间依赖性参数中编码的非平凡动力学希尔伯特空间的非本地性质，该参数取决于复杂频率的假想部分。
In this work we present the general unified description for the unitary time-evolution generated by time-dependent non-Hermitian Hamiltonians embedding the bosonic representations of $\mathfrak{su}(1,1)$ and $\mathfrak{su}(2)$ Lie algebras. We take into account a time-dependent Hermitian Dyson maps written in terms of the elements of those algebras with the relation between non-Hermitian and its Hermitian counterpart being independent of the algebra realization. As a direct consequence, we verify that a time-evolved state of uncoupled modes modulated by a time-dependent complex frequency may exhibits a non-zero entanglement even when the cross-operators, typical of the interaction between modes, are absent. This is due the non-local nature of the non-trivial dynamical Hilbert space metric encoded in the time-dependent parameters of the general Hermitian Dyson map, which depend on the imaginary part of the complex frequency.
