Dynamical recurrence and the quantum control of coupled oscillators.
Dynamical recurrence and the quantum control of coupled oscillators.
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DOI：
10.1103/physrevlett.108.150501
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发表时间：
2011-10
影响因子：
8.6
通讯作者：
M. Genoni;A. Serafini;M. Kim;D. Burgarth
中科院分区：
文献类型：
--
作者：
M. Genoni;A. Serafini;M. Kim;D. Burgarth
可控性-通过应用一组可用操作来执行任何目标动态的可能性-是任何物理系统实际使用的基本要求。对于有限维系统，如自旋系统，建立可控性的精确准则，如所谓的秩准则，是众所周知的。然而，大多数物理系统需要描述的一个无限维希尔伯特空间的可控性了解甚少。在这里，我们研究无限维玻色子量子系统-包括量子光，玻色子原子的合奏，离子的运动自由度，和纳米机械振荡器-由二次哈密顿（这样他们的演变是类似于耦合谐振子）。在突出了Hilbert空间中的能控性和递归性之间的密切联系之后，我们证明了，对于耦合振子，必须满足一个简单的额外条件才能将秩准则扩展到无限维二次系统。此外，我们提出了一个有用的应用，我们的发现，通过证明间接可控的谐振子链。
Controllability--the possibility of performing any target dynamics by applying a set of available operations--is a fundamental requirement for the practical use of any physical system. For finite-dimensional systems, such as spin systems, precise criteria to establish controllability, such as the so-called rank criterion, are well known. However, most physical systems require a description in terms of an infinite-dimensional Hilbert space whose controllability properties are poorly understood. Here, we investigate infinite-dimensional bosonic quantum systems--encompassing quantum light, ensembles of bosonic atoms, motional degrees of freedom of ions, and nanomechanical oscillators--governed by quadratic Hamiltonians (such that their evolution is analogous to coupled harmonic oscillators). After having highlighted the intimate connection between controllability and recurrence in the Hilbert space, we prove that, for coupled oscillators, a simple extra condition has to be fulfilled to extend the rank criterion to infinite-dimensional quadratic systems. Further, we present a useful application of our finding, by proving indirect controllability of a chain of harmonic oscillators.