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arXiv 2201.01773quant-phcond-mat.mes-hall
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准周期和随机噪声对多体动力学解耦协议的影响

Effect of quasiperiodic and random noise on many-body dynamical decoupling protocols

Tristan Martin, Ivar Martin, Kartiek Agarwal

摘要:

对称性(及其自发破裂)可以用来保护和产生新的量子相,并导致有趣的集体现象。在参考文献1中,作者描述了一种通用的动态解耦(多重分形)协议,可用于在多体系统中设计多个离散对称性。目前的工作扩大了前通过研究准周期和随机噪声对这样的动力计划的影响。我们发现,工程对称发生器的松弛一般由以下过程进行:i)微观时间尺度上的初始松弛到其高度与噪声无关的预热平台,ii)具有噪声相关速率的线性松弛制度,然后是iii)仅存在于准周期噪声的慢对数松弛制度。我们收集这些制度的基本特征,通过缩放崩溃,并表明它们可以被解释为一般的频谱特性的各种噪声波形考虑。特别地,准周期噪声的特征在于具有模仿白噪声的噪声基底的高度时间相关的频谱,以及随着时间而变得更尖锐的峰值。我们认为,本底噪声和峰值有助于初始的线性时间松弛,而对数制度开始时,峰值变得足够好地解决,并停止有助于进一步放松。我们提供了数字证据来证明这些发现。

英文摘要:

Symmetries (and their spontaneous rupturing) can be used to protect and engender novel quantum phases and lead to interesting collective phenomena. In Ref. 1, the authors described a general dynamical decoupling (polyfractal) protocol that can be used to engineer multiple discrete symmetries in many-body systems. The present work expands on the former by studying the effect of quasiperiodic and random noise on such a dynamical scheme. We find generally that relaxation of engineered symmetry generators proceeds by i) an initial relaxation on microscopic timescales to a prethermal plateau whose height is independent of noise, ii) a linear relaxation regime with a noise-dependent rate, followed by iii) a slow logarithmic relaxation regime that is only present for quasiperiodic noise. We glean the essential features of these regimes via scaling collapses and show that they can be generally explained by the spectral properties of the various noise waveforms considered. In particular, the quasiperiodic noise is characterised by highly time dependent spectrum with a noise floor that mimics white noise, and peaks that grow sharper with time. We argue that both the noise floor and peaks contribute to the initial linear-in-time relaxation while the logarithmic regime is initiated when the peaks become sufficiently well resolved and cease to contribute to further relaxation. We provide numerical evidence to justify these findings.

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