Effect of Disorder Amplitude on the Transport of Bose Einstein Condensates at Lowest Energy
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Effect of Disorder Amplitude on the Transport of Bose Einstein Condensates at Lowest Energy Yedjour Afifa1 · Mokaddem Allel2 · Bendouma Doumi2,3 Received: 30 July 2020 / Accepted: 19 October 2020 / © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In this paper, we have presented an analytical and numerical study of a matter wave packet propagation in a disordered optical potential. We have used the self-consistent Born approximation which is well supported in weak disorder to calculate the real part of the self- energy R(ε, p). The difference of 0.1 which appears between the analytical and numerical calculation is very acceptable. The varying of disorder amplitude change the position of the critical energy of the transition which it can be larger or smaller than correlation energy. This analysis gives new insight into numerical result. We propose to analyze the behavior of the energy distribution with this quantum corrected diffusion factor, which is a very important parameter for the mobility edge prediction. Our results open new interesting studies and provide good reference data for future research such as the behavior of the mobility edge in fractal systems and the evolution of the density of condensates in time and space. Keywords Disorder amplitude · Mobility edge · Optical speckle · Self-energy
1 Introduction For the last decade, interesting works have been devoted to study the localization phenomenon in 3D mesoscopic systems with all types of coherent waves [1–4]. By now it is well established with both theoretical and experimental works that is a possibility to observe the Anderson transition which is proposed by Anderson in 1958 [5]. However, recently some models of disorder with much weaker interaction were used to track the 3D Anderson localisation. The localisation has been studied theoretically and observed experimentally in: electromagnetic [6], optical [7, 8], acoustic [9] and also, in the cold atom in correlated laser speckle [10–12].
Yedjour Afifa
[email protected] 1
Facult´e de Physique, USTO MB, B.p.1505 El M’Naour, 31000, Oran, Alg´erie
2
Laboratoire d´Instrumentation et Mat´eriaux Avanc´es, Centre Universitaire Nour Bachir El-Bayadh, El-Bayadh, Alg´erie
3
Physics Department, Faculty of Science, University Dr.TaharMoulay of Saida, Saida, Alg´erie
International Journal of Theoretical Physics
The problem posed is the position of the mobility edge that can be determined from the direct measurement of the spectral function A(ε, k) [13]. According to Anderson, a critical energy (mobility edge εc ) exists in 3D which separates extended and localized states. An eigenstate is extended or localized if the corresponding energy is larger or smaller than εc . When the condensate is released from the trap, the atoms achieve kinetic energies up to the chemical potential μ of the trapped condensate. For weak disorder εc < μ, and a fraction of atoms diffuses, whereas the remainder is localized. It was found in the reference [14], that it is possible to numerically
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