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arXiv:0809.5012

Adiabatic Transport of Bose-Einstein Condensate in Double- and Triple-Well Traps

Valentin O. Nesterenko, Novikov, A. N., F. Cruz, Emerson Luiz Lapolli

Published Sep 29, 2008• 0 citations
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Abstract

By using a close similarity between multi-photon and tunneling population transfer schemes, we propose robust adiabatic methods for the transport of Bose-Einstein condensate (BEC) in double- and triple-well traps. The calculations within the mean-field approximation (Gross-Pitaevskii equation) show that irreversible and complete transport takes place even in the presence of the non-linear effects caused by interaction between BEC atoms. The transfer is driven by adiabatic time-dependent monitoring the barriers and well depths. The proposed methods are universal and can be applied to a variety of systems and scenarios.

DOI
10.48550/arxiv.0809.5012

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By using a close similarity between multi-photon and tunneling population transfer schemes, we propose robust adiabatic methods for the transport of Bose-Einstein condensate (BEC) in double- and triple-well traps. The calculations within the mean-field approximation (Gross-Pitaevskii equation) show that irreversible and complete transport takes place even in the presence of the non-linear effects caused by interaction between BEC atoms. The transfer is driven by adiabatic time-dependent monitoring the barriers and well depths. The proposed methods are universal and can be applied to a variety of systems and scenarios.
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A complete adiabatic transport of Bose–Einstein condensate (BEC) in a double-well trap is investigated within the mean field approximation. The transfer is driven by the time-dependent (Gaussian) coupling between the wells and their relative detuning. The protocol successfully works in a wide range of both repulsive and attractive BEC interaction. The nonlinear effects caused by the interaction can be turned from detrimental into favourable for the transport. The results are compared with familiar Landau–Zener scenarios using the constant coupling. It is shown that the pulsed Gaussian coupling provides a new transport regime where coupling edges are decisive and convenient switch of the transport is possible.
Two aspects of the transport of the repulsive Bose-Einstein condensate (BEC) in a double-well trap are inspected: impact of the interatomic interaction and analogy to the Josephson effect. The analysis employs a numerical solution of 3D time-dependent Gross-Pitaevskii equation for a total order parameter covering all the trap. The population transfer is driven by a time-dependent shift of a barrier separating the left and right wells. Sharp and soft profiles of the barrier velocity are tested. Evolution of the relevant characteristics, involving phase differences and currents, is inspected. It is shown that the repulsive interaction substantially supports the transfer making it possible i) in a wide velocity interval and ii) three orders of magnitude faster than in the ideal BEC. The transport can be approximately treated as the d.c. Josephson effect. A dual origin of the critical barrier velocity (break of adiabatic following and d.c.-a.c. transition) is discussed. Following the calculations, robustness of the transport (d.c.) crucially depends on the interaction and barrier velocity profile. Only soft profiles which minimize undesirable dipole oscillations are acceptable.
The irreversible transport of multi-component Bose-Einstein condensate (BEC) is investigated within the Stimulated Raman Adiabatic Passage (STIRAP) scheme. A general formalism for a single BEC in M -well trap is derived and analogy between multi-photon and tunneling processes is demonstrated. STIRAP transport of BEC in a cyclic triple-well trap is explored for various values of detuning and interaction between BEC atoms. It is shown that STIRAP provides a complete population transfer at zero detuning and interaction and persists at their modest values. The detuning is found not to be obligatory. The possibility of non-adiabatic transport with intuitive order of couplings is demonstrated. Evolution of the condensate phases and generation of dynamical and geometric phases are inspected. It is shown that STIRAP allows to generate the unconventional geometrical phase which is now of a keen interest in quantum computing.
An inverse population transfer of the repulsive Bose-Einstein condensate (BEC) in a weakly bound double-well trap is explored within the 3D time-dependent Gross-Pitaevskii equation. The model avoids numerous common approximations (two-mode treatment, time-space factorization, etc) and closely follows the conditions of Heidelberg experiments, thus providing a realistic description of BEC dynamics. The transfer is driven by a time-dependent shift of a barrier separating the left and right wells. It is shown that completeness and robustness of the process considerably depend on the amplitude and time profile of the shift velocity. Soft profiles provide the most robust inversion. The repulsive interaction substantially supports the transfer making it possible i) in a wide velocity interval and ii) three orders of magnitude faster than in the ideal BEC.
A complete adiabatic transport of Bose-Einstein condensate in a double-well trap is investigated within the Landau-Zener (LZ), and Gaussian Landau-Zener (GLZ) schemes for the case of a small non-linearity, when the atomic interaction is weaker than the coupling. The schemes use the constant (LZ) and time-dependent Gaussian (GLZ) couplings. The mean field calculations show that LZ and GLZ suggest essentially different transport dynamics. Significant deviations from the case of a strong coupling are discussed.