Shortcuts to adiabaticity for an interacting BoseEinstein condensate via exact solutions of the generalized Ermakov equation
Abstract
Shortcuts to adiabatic expansion of the effectively onedimensional BoseEinstein condensate (BEC) loaded in the harmonicoscillator (HO) trap are investigated by combining techniques of variational approximation and inverse engineering. Piecewiseconstant (discontinuous) intermediate trap frequencies, similar to the known bangbang forms in the optimalcontrol 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 shortcuttoadiabaticity 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.
 Publication:

Chaos
 Pub Date:
 May 2020
 DOI:
 10.1063/5.0004309
 arXiv:
 arXiv:2002.03632
 Bibcode:
 2020Chaos..30e3131H
 Keywords:

 Quantum Physics;
 Condensed Matter  Quantum Gases;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 9 pages, 6 figures, to be published in Chaos