低温声腔中基于二能级系统与高频泛音相互作用引起的声学声子损失

南京大学学报(自然科学版) ›› 2015, Vol. 51 ›› Issue (6): 1120–1125.

低温声腔中基于二能级系统与高频泛音相互作用引起的声学声子损失

李国龙1，任中洲1,2,3

出版日期:2015-11-09 发布日期:2015-11-09
作者简介:(1. 南京大学物理学系与近代声学教育部重点实验室,南京,210093;2. 南京大学核物理科学与技术联合研究中心,南京,210009;3. 国家重离子加速器实验室理论核物理中心,兰州,730000)
基金资助:
国家973基础研究与开发(2013CB834400，2010CB327803)，国家自然科学基金(11035001，11375086，11105079，10975072) ，博士点研究资金(20100091110028)，澳门科技发展资金(068/2011/A)

Acoustic phonon losses due to the interaction of two-level Systems with high overtones in cryogenic acoustic cavities

Li Guolong1, Ren Zhongzhou1,2,3*

Online:2015-11-09 Published:2015-11-09
About author:(1. Key Laboratory of Modern Acoustics and Department of Physics, Nanjing University, Nanjing, 210093, China; 2. Joint Center of Nuclear Science and Technology, Nanjing University, Nanjing, 210093, China; 3. Center of Theoretical Nuclear Physics, National Laboratory of Heavy-Ion Accelerator, Lanzhou, 730000, China)

摘要/Abstract

摘要： 在晶体中，杂质原子或晶格缺陷形成的二能级系统会对声子产生弹性散射。利用压电晶体作为共振腔的低温声腔中，这种散射过程的存在导致高频泛音的损失。这种散射可以解释为压电晶体中应变场与二能级系统的耦合，并且能够用一个相互作用哈密顿量描述。根据这个相互作用哈密顿量和二阶微扰论，我们得到了一个基于声子-二能级系统弹性散射的声子损失公式。根据这个公式，我们得到了声波损失如何受声波频率和环境温度的变化，而这种分析给出了一个合理的损失机制，解释了最近一个测量高频泛音品质因子的实验[M. Goryachev et al., Phys. Rev. Lett. 111, 085502 (2013)]。我们希望我们的工作可以为降低低温声腔激发的高频声波损失提供了理论支持。

Abstract: The purpose of this work is to provide a reason explanation for an experiment which measures the quality factor of bulk acoustic wave excited by the cryogenic acoustic cavities[M. Goryachev et. al., Physics Review Letters: volume111, 085502 (2013)]. We demonstrate that two-level systems (TLSs), which are caused by impurity atoms or lattice defects, lead to a kind of acoustic phonon elastic scattering.As a result, this kind of scattering processes result in an attenuation of high overtones in cryogenic acoustic cavities made of piezoelectric crystals. The elastic scattering between phonons and TLSs can be interpreted as the coupling between strain field and TLSs in acoustic cavities, which can be described by an interaction Hamiltonian. Based on this interaction Hamiltonian and the second-order perturbation theory, we obtain a formula of the attenuation resulted from the acoustic wave elastic scattering by TLSs. Consequently, we show how input frequency of the excited acoustic wave and environmental temperature influence this attenuation. Such analysis gives a reasonable loss mechanism for the recent experiment. Firstly, our theory provides an?interpretation for the law that the qualityfactorQ is inversely proportional?to?third power of frequency, i.e., Q?f3=const. This law is different from usual frequency dependences which derive from other usual loss mechanisms, such as phonon-phonon interactions and thermoelastic damping. Secondly, our formula expresses an abnormal temperature tendency that the Q factor tends to lower with an increase of temperature. It violates general loss feature, but consists with the temperature tendency as the experience shows. We believe that our work offers a useful support for decreasing the losses for excited high-frequency acoustic wave in cryogenic acoustic cavities

李国龙1，任中洲1,2,3. 低温声腔中基于二能级系统与高频泛音相互作用引起的声学声子损失[J]. 南京大学学报(自然科学版), 2015, 51(6): 1120–1125.

Li Guolong1, Ren Zhongzhou1,2,3*. Acoustic phonon losses due to the interaction of two-level Systems with high overtones in cryogenic acoustic cavities[J]. Journal of Nanjing University(Natural Sciences), 2015, 51(6): 1120–1125.

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