arXiv 1111.56272011-11-23quant-ph

原子系综的连续测量量子态层析成像

Continuous Measurement Quantum State Tomography of Atomic Ensembles

Carlos A. Riofrío

备注：: Ph.D. Dissertation

摘要：

量子态层析成像是量子信息处理的基本工具。它允许我们通过测量系统的许多相同准备的副本上的不同可观测量来估计量子系统的状态。一般来说，这是一项非常耗时的任务，需要进行大量的测量。然而，存在可以更有效地完成数据采集的系统。事实上，量子系统的系综可以被外部场准备和操纵，同时被连续和集体探测，产生足够的信息来估计其状态。这为连续测量量子层析成像提供了基础。在这个协议中，一个合奏的同样准备的系统共同探测和控制的时间依赖性的方式，以创建一个信息完整的连续测量记录。然后将测量历史反转以确定初始时刻的状态。我们使用两种不同的估计方法：极大似然和压缩感知。一般形式主义的情况下，适用于重建的量子态编码的大自旋碱金属原子，${}^{133}$ Cs的磁性子能级。我们将此协议的情况下，在全16维电子地面子空间（$F=3 \oplus F=4$），微波和射频磁场控制的状态重建。我们提出了一个实验演示连续测量量子层析成像在冷铯原子系综完全控制其16维希尔伯特空间。我们展示了在实验室中实现的精致的控制水平，以及本文中讨论的理论与实验结果之间的良好一致性。这使我们能够实现低复杂度量子态的量子效率>95%，以及任意随机态的量子效率>92%，这对于这种大小的空间来说是一个巨大的成就。

英文摘要：

Quantum state tomography is a fundamental tool in quantum information processing. It allows us to estimate the state of a quantum system by measuring different observables on many identically prepared copies of the system. This is, in general, a very time-consuming task that requires a large number of measurements. There are, however, systems in which the data acquisition can be done more efficiently. In fact, an ensemble of quantum systems can be prepared and manipulated by external fields while being continuously and collectively probed, producing enough information to estimate its state. This provides a basis for continuous measurement quantum tomography. In this protocol, an ensemble of identically prepared systems is collectively probed and controlled in a time-dependent manner to create an informationally complete continuous measurement record. The measurement history is then inverted to determine the state at the initial time. We use two different estimation methods: maximum likelihood and compressed sensing. The general formalism is applied to the case of reconstruction of the quantum state encoded in the magnetic sub-levels of a large-spin alkali atom, ${}^{133}$Cs. We apply this protocol to the case of reconstruction of states in the full 16-dimensional electronic-ground subspace ($F=3 \oplus F=4$), controlled by microwaves and radio-frequency magnetic fields. We present an experimental demonstration of continuous measurement quantum tomography in an ensemble of cold cesium atoms with full control of its 16-dimensional Hilbert space. We show the exquisite level of control achieved in the lab and the excellent agreement between the theory discussed in this dissertation and the experimental results. This allows us to achieve fidelities >95% for low complexity quantum states, and >92% for arbitrary random states, which is a formidable accomplishment for a space of this size.

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