[论文解读] Generalized Collective States and Their Role in a Collective State Atomic Interferometer and Atomic Clock

Resham Sarkar, May E. Kim+3 more|arXiv (Cornell University)|Aug 11, 2014

Cold Atom Physics and Bose-Einstein Condensates被引用 2

一句话总结

本文提出了一套广义框架，用于描述在激光激发下非相互作用原子系综中的集体态，考虑了空间变化的拉比频率、多普勒频移和激光相位。研究展示了在非理想条件下对称与非对称集体态的形成机制，给出了广义对称态的显式振幅计算，并表明吸收光子的集体态对应于希尔伯特空间中的多维旋转，从而为集体态原子干涉仪和时钟提供了更精确的建模方法，显著降低了量子投影噪声。

ABSTRACT

We investigate the behavior of an ensemble of N non-interacting, identical atoms, excited by a laser with a wavelength of λ. In general, the i-th atom sees a Rabi frequency Ωi, an initial position dependent laser phase φi, and a motion induced Doppler shift of δi. When Ωi = Ω and δi = δ for all atoms, the system evolves into a superposition of (N + 1) generalized symmetric collective states, independent of the values of φi. If φi = φ for all atoms, these states simplify to the well known Dicke collective states. When Ωi or δi is distinct for each atom, the system evolves into a superposition of symmetric as well as asymmetric collective states. For a large value of N , the number of asymmetric states (2 − (N + 1)) is far greater than that of the symmetric states. For a collective state atomic interferometer (CSAI) and a collective state atomic clock (CSAC) we recently proposed, it is important to understand the behavior of all the collective states under various conditions. In this paper, we show how to formulate the properties of all the collective states under various non-idealities, and use this formulation to understand the dynamics thereof. Specifically, for the case where Ωi = Ω and δi = δ for all atoms, we show how the amplitudes of each of the generalized collective states can be determined explicitly in a simple manner. For the case where Ωi or δi is distinct for each atom, we show how the symmetric and asymmetric collective states can be treated on the same footing. Furthermore, we show that the collective states corresponding to the absorption of a given number of photons can be visualized as an abstract, multi-dimensional rotation in the Hilbert space spanned by the ordered product states of individual atoms. We also consider the effect of treating the center of mass degree of freedom of the atoms quantum mechanically on the description of the collective states. In particular, we show that it is indeed possible to construct a generalized collective state, as needed for the CSAI, when each atom is assumed to be in a localized wave packet. The analysis presented in this paper is crucial to understanding the dynamics of both the CSAI and the CSAC, which in turn represent radically new developments in the area of opto-atomic metrology, with significant improvement in precision over the state of the art. Furthermore, it opens up new avenues for exploring reduction of quantum projection noise via spin squeezing.

研究动机与目标

• 开发一个全面的理论框架，用于描述在非理想激光激发条件下原子系综中广义集体态的特性。
• 理解当拉比频率或多普勒频移在原子间变化时，对称与非对称集体态的动力学行为。
• 通过引入真实实验中的非理想因素，实现对集体态原子干涉仪（CSAI）和集体态原子钟（CSAC）的精确建模。
• 探讨量子质心运动在定义集体态中的作用，特别是当原子处于局域波包状态时的情形。
• 为下一代光原子传感器中通过自旋压缩实现噪声抑制奠定理论基础。

提出的方法

• 采用广义对称基来形式化集体态，以容纳空间变化的拉比频率（Ωi）、初始相位（φi）和多普勒频移（δi）。
• 推导出当所有原子满足 Ωi = Ω 且 δi = δ 时，广义对称集体态振幅的显式表达式。
• 通过将形式体系扩展至原子特异性 Ωi 或 δi 的情况，统一处理对称与非对称集体态。
• 将集体态演化表示为有序乘积态希尔伯特空间中的多维旋转，对应于光子数跃迁。
• 通过将每个原子建模为局域波包，引入量子力学质心运动，并在此条件下构建广义集体态。
• 利用群论与多体量子力学技术，分析在非理想条件下集体态的结构与演化。

实验结果

研究问题

• RQ1 非均匀的拉比频率与多普勒频移如何影响原子系综中集体态的形成与演化？
• RQ2 在非理想激发条件下，能否在单一统一的形式体系下处理对称与非对称集体态？
• RQ3 集体态演化在希尔伯特空间中的多维旋转几何意义是什么？
• RQ4 将质心运动以量子力学方式处理，如何影响集体态的定义与动力学？
• RQ5 广义集体态形式体系在多大程度上可通过自旋压缩实现原子干涉仪与原子钟中的噪声抑制？

主要发现

• 当所有原子经历相同的拉比频率与多普勒频移时，系统演化为 (N + 1) 个广义对称集体态的叠加，且该结果与初始相位变化无关。
• 当所有原子的 Ω 与 δ 相同时，每个广义集体态的振幅可被显式且简洁地确定，从而实现精确的态制备与分析。
• 当拉比频率或多普勒频移按原子个体变化时，非对称集体态的数量增长为 2^N − (N + 1)，对于大 N 值，远超对称态的数量。
• 对应于吸收固定光子数的集体态，在乘积态希尔伯特空间中几何上等价于多维旋转。
• 即使每个原子被建模为局域波包，仍可构建广义集体态，验证了该形式体系在具有量子质心运动的真实实验设置中的适用性。
• 所发展的形式体系深化了对集体态原子干涉仪与原子钟中动力学行为的理解，为通过自旋压缩实现量子投影噪声降低铺平了道路。