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

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Journal of Nanjing University(Natural Sciences) ›› 2015, Vol. 51 ›› Issue (6) : 1120-1125.

Li Guolong1, Ren Zhongzhou1,2,3*

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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

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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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