Self-energy of cold atoms in a long-range disordered optical potential
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- 作者：A. Yedjour ; S. Bahlouli ; B. Doumi ; A. Mokaddem…
- 关键词：Bose–Einstein condensate ; Optical speckle ; Weak localization ; Self ; energy
- 刊名：Journal of Computational Electronics
- 出版年：2017
- 出版时间：March 2017
- 年：2017
- 卷：16
- 期：1
- 页码：18-23
- 全文大小：
- 刊物类别：Engineering
- 刊物主题：Appl.Mathematics/Computational Methods of Engineering; Electrical Engineering; Theoretical, Mathematical and Computational Physics; Optical and Electronic Materials; Mechanical Engineering;
- 出版者：Springer US
- ISSN：1572-8137
- 卷排序：16
文摘
We study the effect of correlation on the expansion of a Bose–Einstein condensate (BEC) released from a harmonic trap. We go beyond the first-order Born approximation (FBA) to use the self-consistent Born approximation (SCBA) to calculate the self-energy \(\Sigma (\varepsilon , k)\) of an atom in a speckle potential with constant amplitude of disorder. For very cold atoms (\(k= 0\)), low chemical potential \(\mu \ll \varepsilon _{\xi }\), and \(U/ \varepsilon ^{2}_{\xi } = 1\), the self-energy spectrum is wide when calculated in the SCBA compared with the FBA. The SCBA locates the band edge at somewhat higher energy, giving rise to many localized atoms. We focus mainly on the energy distribution at \(k = 0\) as expressed by the spectral function. Our numerical results show that the spectral function of the expanding atoms as calculated in the FBA at \(\varepsilon = 0\) has low weight and extends up to \(\varepsilon = 4 \varepsilon _{\xi }\). When using the SCBA, the behavior of the energy distribution for low chemical potential is different, showing a continuum, while a large weight corresponding to \(\varepsilon \) shifts the spectrum of negative energy values to \(\frac{\varepsilon }{\varepsilon _\xi } = -0.78\) and the energy distribution is near unity. We show that the form of the density of states locates the mobility near \(\varepsilon = - \varepsilon _\xi \). At \(\varepsilon = 0\), we obtain 35 % of delocalized atoms. We conclude that correlation disorder seems to help localize atoms with energy below zero. In particular, we show that the negative energy values observed in the energy spectrum imply that the probability of finding an atom with energy \(\varepsilon _\xi \) around \(\varepsilon \) is conserved.