Shortcuts to adiabatic expansion of the effectively one-dimensional Bose–Einstein condensate (BEC) loaded in the harmonic-oscillator (HO) trap are investigated by combining techniques of variational approximation and inverse engineering. Piecewise-constant (discontinuous) intermediate trap frequencies, similar to the known bang–bang forms in the optimal-control theory, are derived from an exact solution of a generalized Ermakov equation. Control schemes considered in the paper include imaginary trap frequencies at short time scales, i.e., the HO potential replaced by the quadratic repulsive one. Taking into regard the BEC’s intrinsic nonlinearity, results are reported for the minimal transfer time, excitation energy (which measures deviation from the effective adiabaticity), and stability for the shortcut-to-adiabaticity protocols. These results are not only useful for the realization of fast frictionless cooling, but also help us to address fundamental problems of the quantum speed limit and thermodynamics.
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Research Article|
May 18 2020
Shortcuts to adiabaticity for an interacting Bose–Einstein condensate via exact solutions of the generalized Ermakov equation
Special Collection:
Instabilities and Nonequilibrium Structures
Tang-You Huang
;
Tang-You Huang
1
International Center of Quantum Artificial Intelligence for Science and Technology (QuArtist) and Department of Physics, Shanghai University
, 200444 Shanghai, China
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Boris A. Malomed
;
Boris A. Malomed
2
Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, and Center for Light-Matter Interaction, Tel Aviv University
, P.O. Box 39040, Ramat Aviv, Tel Aviv, Israel
3
Instituto de Alta Investigación, Universidad de Tarapacá
, Casilla 7D, Arica, Chile
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Xi Chen
Xi Chen
a)
1
International Center of Quantum Artificial Intelligence for Science and Technology (QuArtist) and Department of Physics, Shanghai University
, 200444 Shanghai, China
4
Department of Physical Chemistry, University of the Basque Country UPV/EHU
, Apartado 644, 48080 Bilbao, Spain
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a)
Author to whom correspondence should be addressed: xchen@shu.edu.cn
Note: This article is part of the Focus Issue, Instabilities and Nonequilibrium Structures.
Chaos 30, 053131 (2020)
Article history
Received:
February 11 2020
Accepted:
April 28 2020
Citation
Tang-You Huang, Boris A. Malomed, Xi Chen; Shortcuts to adiabaticity for an interacting Bose–Einstein condensate via exact solutions of the generalized Ermakov equation. Chaos 1 May 2020; 30 (5): 053131. https://doi.org/10.1063/5.0004309
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