标题： 外激振子的涌现熵和三波混频过程中的压缩特性 显示英文标题

标题： Emergent entropy of exotic oscillators and squeezing in three-wave mixing process

摘要： 我们通过计算约化密度矩阵的冯·诺依曼熵来证明放置在非交换Moyal平面上的一组谐振子的空间自由度之间的纠缠存在性（“ exotic 振子”）。 明确验证了这种纠缠来源于非交换性，而非交换性控制着空间模式之间的耦合强度。 这种情况可以轻松推广到动量分量也满足非交换关系的情形，从而整个相空间变为非交换的。 在前一种情况下，即仅存在空间非交换性时，潜在的数学结构类似于由Rindler观察者观测到的Unruh效应，此时加速与非交换参数相关联。 证明了在存在谐波相互作用的情况下Landau问题给出了这一效应的具体物理实现。 最后，我们表明相空间非交换性可以导致一种非经典的压缩效应，该效应源于三波混频过程中介质的非线性。 显示英文摘要

摘要： We demonstrate the existence of entanglement between the spatial degrees of freedom of a system of harmonic oscillators placed in the noncommutative Moyal plane ("exotic oscillators") by computing the entanglement entropy as measured by the von Neumann entropy of the reduced density matrix. It is explicitly verified that the entanglement arises from the noncommutativity, which controls the coupling strength between the spatial modes. This can easily be generalised to the case where the momentum components also satisfy noncommutative relations, so that the entire phase space becomes noncommutative. In the former case, i.e. when only the spatial noncommutativity is present, the underlying mathematical structure is reminiscent of the Unruh effect, as observed by a Rindler observer whose acceleration now gets related to the noncommutative parameter. It is shown that the Landau problem in the presence of a harmonic interaction gives a concrete physical realisation of this effect. Finally, we show that phase-space noncommutativity can give rise to a the non-classical effect of squeezing, which results from the non-linearity of a medium in a three-wave mixing process.