Landau damping and frequency-shift of (0, 0, 2) scissors mode in a disc-shaped Bose-Einstein condensate

Zhao Jun-Ya; Li Chen-Xu; Ma Xiao-Dong

doi:10.7498/aps.68.20190661

Abstract

By using the Hartree-Fock-Bogoliubov approximation of mean-field theory and the analytic method based on Thomas-Feimi approximation, the Landau damping and frequency-shift of (0, 0, 2) scissors mode in a disc-shaped Bose-Einstein condensate are investigated and the damping rate and frequency-shift magnitude as well as their temperature dependence are calculated. In the calculation, the practical relaxations of the elementary excitations and the orthometric relation among the relaxations are considered in the relation for the perturbed eigenfrequency of mean-field theory to obtain the calculation formula of damping and frequency-shift, and the first-order approximation of Gaussian distribution function is employed for the ground-state wavefunction to eliminate the divergence of the three-mode coupling matrix elements in Thomas-Fermi approximation. Taking the same parameters of particle number, trapping frequency and anisotropy as those in relevent experiment research, our theoretical calculation results accord with the relevent experimental measurement results. Because of the complexity of the theory and the difficulty of calculation, most of mean-field theory researches on damping and frequency shift of collective excitation in one and two component Bose-Einstein condensates adopt semi-classical approximation, the quasi-particle excitation spectrum is regarded as continuously integrating each quasi-particle transition contribution to damping and frequency shift. In this paper, the damping and frequency shift are calculated according to the discrete quasi-particle excitation spectrum, and in the course of the study the improving of method of considering the practical relaxations of the elementary excitations and the orthometric relation among the relaxations is put forward. It is hoped that the method will have some reference value in the future work.

Keywords:

Authors and contacts

1.
College of Physics and Electronic Engineering, Xinjiang Normal University, Urumchi 830054, China
2.
School of Medical Engineering and Technology, Xinjiang Medical University, Urumchi 830011, China

Corresponding author: Ma Xiao-Dong, xdma07@aliyun.com

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 10864006, 11264039), the Key Research Project of Xinjiang Higher Education, China (Grant No. XJEDU20141029), the “Physics” Specialty of Xinjiang Normal University, China, and the Key Subject of “Physics” in Xinjiang Normal University, China

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References

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Cited By

图 1 以跃迁频率$\gamma_{ij}$为变量的剪刀模阻尼强度$\omega_{ij}$函数线状图

Figure 1. Histogram of damping strength $\gamma_{ij}$ as a function of the transition $\omega_{ij}$ for the scissors mode in the condensate.

DownLoad: Full-Size Img PowerPoint

图 2 以跃迁频率$ \gamma_{ij} $为变量的剪刀模阻尼强度$ \omega_{ij} $函数线状图 ($ \omega_{ij}/\omega_{\rm ho} $取值范围为0—1.6)

Figure 2. Histogram of damping strength $ \gamma_{ij} $ as a function of the transition $ \omega_{ij} $ for the scissors mode in the condensate, ($ \omega_{ij}/\omega_{\rm ho} $= 1–1.6).

DownLoad: Full-Size Img PowerPoint

图 3 朗道阻尼系数$ \gamma_{0} $随$ \gamma $变化函数图

Figure 3. The $ \gamma_{0} $ as a function of $ \gamma $ for the Landau damping rate.

DownLoad: Full-Size Img PowerPoint

图 4 凝聚体集体模的频移(a)和朗道阻尼系数(b)随温度T变化

Figure 4. The frequency-shift (a) and the Landau damping rate $ \gamma_{0} $ (b) of the collective mode in the condensate as a function of the temperature T.

DownLoad: Full-Size Img PowerPoint

map

[1]	Pethick C J, Smith H 2008 Bose-Einstein Condensation in Dilute Gases (2nd Ed.) (Cambridge: Cambridge University Press) p23
[2]	Dalfovo F, Minniti C, Pitaevskii L P 1997 Phys. Rev. A 56 4855 Google Scholar
[3]	Morgan S A, Choi S, Burnett K, Edwards M 1998 Phys. Rev. A 57 3818 Google Scholar
[4]	Hechenblaikner G, Maragò O M, Hodby E, Arlt J, Hopkins S, Foot C J 2000 Phys. Rev. Lett. 85 692 Google Scholar
[5]	Hodby E, Maragò O M, Hechenblaikner G, Foot C J 2001 Phys. Rev. Lett. 86 2196 Google Scholar
[6]	Edwards M, Dodd R J, Chark C W, Ruprecht P A, Burnett K 1996 Phys. Rev. A 53 R1950 Google Scholar
[7]	Maragò O M, Hopkins S A, Arlt J, Hodby E, Hechenblaikner G, Foot C J 2000 Phys. Rev. Lett. 84 2056 Google Scholar
[8]	Khawaja U A, Stoof H T C 2001 Phys. Rev. A 65 013605 Google Scholar
[9]	Hechenblaikner G, Morgan S A, Hodby E, Maragò O M, Foot C J 2002 Phys. Rev. A 65 033612 Google Scholar
[10]	Bijlsma M J, Stoof H T C 1999 Phys. Rev. A 60 3973 Google Scholar
[11]	Öhberg P, Stenholm S 1998 Phys. Rev. A 57 1272 Google Scholar
[12]	Stringari S 1996 Phys. Rev. Lett. 77 2360 Google Scholar
[13]	Fetter A L 1996 Phys. Rev. A 53 4245 Google Scholar
[14]	Shchedrin G, Jaschke D, Carr L D 2018 Sci. Rep. 8 11523 Google Scholar
[15]	Ota M, Larcher F, Dalfovo F, Pitaevskii L, Proukakis N P, Stringari S 2018 Phys. Rev. Lett. 121 145302 Google Scholar
[16]	Mendonca J T, Tercas H, Gammal A 2018 Phys. Rev. A 97 063610 Google Scholar
[17]	Cappellaro A, Toigo F, Salasnich L 2018 Phys. Rev. A 98 043605 Google Scholar
[18]	席忠红, 杨雪滢, 唐娜, 宋琳, 李晓霖, 石玉仁 2018 67 230501 Google Scholar Xi Z H, Yang X Y, Tang N, Song L, Li X L, Shi Y R 2018 Acta Phys. Sin. 67 230501 Google Scholar
[19]	Zhu K Q, Yu Z F, Gao J M, Zhang A X, Xu H P, Xue J K 2019 Chin. Phys. B 28 010307 Google Scholar
[20]	李吉, 刘伍明 2018 67 110302 Google Scholar Li J, Liu W M 2018 Acta Phys. Sin. 67 110302 Google Scholar
[21]	Zhou W Y, Wu Y J, Kou S P 2018 Chin. Phys. B 27 050302 Google Scholar
[22]	Ma Y L, Chui S T 2002 Phys. Rev. A 65 053610 Google Scholar
[23]	Hu B, Huang G, Ma Y L 2004 Phys. Rev. A 69 063608 Google Scholar
[24]	Maragò O, Hechenblaikner G, Hodby E, Foot C 2001 Phys. Rev. Lett. 86 3938 Google Scholar
[25]	Stamper-Kurn D M, Miesner H J, Inouye S, Andrews M R, Ketterle W 1998 Phys. Rev. Lett. 81 500 Google Scholar
[26]	Chevy F, Bretin V, Rosenbusch P, Madison K W, Dalibard J 2002 Phys. Rev. Lett. 88 250402 Google Scholar
[27]	Jin D S, Matthews M R, Ensher J R, Wieman C E, Cornell E A 1997 Phys. Rev. Lett. 78 764 Google Scholar
[28]	Zaremba E, Griffin A, Nikuni T 1998 Phys. Rev. A 57 4695 Google Scholar
[29]	Zaremba E, Nikuni T, Griffin A 1999 J. Low. Temp. Phys. 116 277 Google Scholar
[30]	Jackson B, Zaremba E 2002 Phys. Rev. Lett. 88 180402 Google Scholar
[31]	Jackson B, Zaremba E 2002 Phys. Rev. Lett. 89 150402 Google Scholar
[32]	Guilleumas M, Pitaevskii L P 1999 Phys. Rev. A 61 013602 Google Scholar
[33]	Das K, Bergeman T 2001 Phys. Rev. A 64 013613 Google Scholar
[34]	Pitaevskii L P, Stringari S 1997 Phys. Lett. A 235 398 Google Scholar
[35]	Fedichev P O, Shlyapnikov G V, Walraven J T M 1998 Phys. Rev. Lett. 80 2269 Google Scholar
[36]	Reidl J, Csordás A, Graham R, Szépfalusy P 2000 Phys. Rev. A 61 043606 Google Scholar
[37]	Mizushima T, Ichioka M, Machida K 2003 Phys. Rev. Lett. 90 180401 Google Scholar
[38]	Morgan S A, Rusch M, Hutchinson D A W, Burnett K 2003 Phys. Rev. Lett. 91 250403 Google Scholar
[39]	Giorgini S 1998 Phys. Rev. A 57 2949 Google Scholar
[40]	Giorgini S 2000 Phys. Rev. A 61 063615 Google Scholar
[41]	Ma X, Ma Y L, Huang G 2007 Phys. Rev. A 75 013628 Google Scholar
[42]	柴兆亮, 周昱, 马晓栋 2013 62 130307 Google Scholar Chai Z L, Zhou Y, Ma X D 2013 Acta Phys. Sin. 62 130307 Google Scholar
[43]	Rahmut A, Peng S Q, Ma X D 2014 Chin. Phys. B 23 090311 Google Scholar
[44]	彭胜强, 阿孜古丽·马合木提, 马晓栋 2015 原子与分子 32 1018 Google Scholar Peng S Q, Rahmut A, Ma X D 2015 J. At. Mol. Phys. 32 1018 Google Scholar
[45]	Bhattacherjee A B 2014 Mode. Phys. Lett. B 28 1450029 Google Scholar
[46]	Natu S S, Wilson R M 2013 Phys. Rev. A 88 063638 Google Scholar
[47]	Moniri S M, Yavari H, Darsheshdar E 2016 Eur. Phys. J. Plus. 131 363 Google Scholar
[48]	Moniri S M, Yavari H, Darsheshdar E 2016 Chin. Phys. B 25 126701 Google Scholar

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Vol. 68, Issue 23 - 2019-12-05

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