{"title":"Decay and revival dynamics of a quantum state embedded in a regularly spaced band of states","authors":"Jan Petter Hansen, Konrad Tywoniuk","doi":"10.1103/physreva.108.053707","DOIUrl":null,"url":null,"abstract":"The dynamics of a single quantum state embedded in one continuum or several (quasi)continua is one of the most studied phenomena in quantum mechanics. In this paper we investigate its discrete analog and consider short- and long-time dynamics based on numerical and analytical solutions of the Schr\\\"odinger equation. In addition to derivation of explicit conditions for initial exponential decay, it is shown that a recent model of this class [L. Guo, A. Grimsmo, A. F. Kockum, M. Pletyukhov, and G. Johansson, Phys. Rev. A 95, 053821 (2017)], describing a qubit coupled to a phonon reservoir with energy dependent coupling parameters, is identical to a qubit interacting with a finite number of parallel regularly spaced bands of states via constant couplings. As a consequence, the characteristic near periodic initial-state revivals can be viewed as a transition of probability between different continua via the reviving initial state. Furthermore, polynomial decay of the reviving peaks is present in any system with constant and sufficiently strong coupling.","PeriodicalId":20121,"journal":{"name":"Physical Review","volume":" 48","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical Review","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1103/physreva.108.053707","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
The dynamics of a single quantum state embedded in one continuum or several (quasi)continua is one of the most studied phenomena in quantum mechanics. In this paper we investigate its discrete analog and consider short- and long-time dynamics based on numerical and analytical solutions of the Schr\"odinger equation. In addition to derivation of explicit conditions for initial exponential decay, it is shown that a recent model of this class [L. Guo, A. Grimsmo, A. F. Kockum, M. Pletyukhov, and G. Johansson, Phys. Rev. A 95, 053821 (2017)], describing a qubit coupled to a phonon reservoir with energy dependent coupling parameters, is identical to a qubit interacting with a finite number of parallel regularly spaced bands of states via constant couplings. As a consequence, the characteristic near periodic initial-state revivals can be viewed as a transition of probability between different continua via the reviving initial state. Furthermore, polynomial decay of the reviving peaks is present in any system with constant and sufficiently strong coupling.
嵌入在一个连续或几个(准)连续中的单个量子态的动力学是量子力学中研究最多的现象之一。本文基于Schr\ odinger方程的数值解和解析解研究了它的离散模拟,并考虑了它的短期和长期动力学。除了推导初始指数衰减的显式条件外,还证明了这类最近的一个模型[L]。郭,A. Grimsmo, A. F. Kockum, M. Pletyukhov和G. Johansson,物理学家。[j],描述了一个量子比特与一个具有能量依赖耦合参数的声子库耦合,与一个量子比特通过恒定耦合与有限数量的平行规则间隔的状态带相互作用相同。因此,近周期初始状态恢复的特征可以看作是通过恢复初始状态在不同连续体之间的概率转移。此外,在任何具有恒定和足够强耦合的系统中,都存在恢复峰的多项式衰减。