TY - JOUR
T1 - Efficient manipulation of Bose–Einstein Condensates in a double-well potential
AU - Adriazola, Jimmie
AU - Goodman, Roy
AU - Kevrekidis, Panayotis
N1 - Funding Information:
This material is based upon work supported by the US National Science Foundation under Grants No. DMS-1809074 and PHY-2110030 (P.G.K.).
Publisher Copyright:
© 2023
PY - 2023/7
Y1 - 2023/7
N2 - We pose the problem of transferring a Bose–Einstein Condensate (BEC) from one side of a double-well potential to the other as an optimal control problem for determining the time-dependent form of the potential. We derive a reduced dynamical system using a Galerkin truncation onto a finite set of eigenfunctions and find that including three modes suffices to effectively control the full dynamics, described by the Gross–Pitaevskii model of BEC. The functional form of the control is reduced to finite dimensions by using another Galerkin-type method called the chopped random basis (CRAB) method, which is then optimized by a genetic algorithm called differential evolution (DE). Finally, we discuss the extent to which the reduction-based optimal control strategy can be refined by means of including more modes in the Galerkin reduction.
AB - We pose the problem of transferring a Bose–Einstein Condensate (BEC) from one side of a double-well potential to the other as an optimal control problem for determining the time-dependent form of the potential. We derive a reduced dynamical system using a Galerkin truncation onto a finite set of eigenfunctions and find that including three modes suffices to effectively control the full dynamics, described by the Gross–Pitaevskii model of BEC. The functional form of the control is reduced to finite dimensions by using another Galerkin-type method called the chopped random basis (CRAB) method, which is then optimized by a genetic algorithm called differential evolution (DE). Finally, we discuss the extent to which the reduction-based optimal control strategy can be refined by means of including more modes in the Galerkin reduction.
KW - Galerkin methods
KW - Hamiltonian dynamical systems
KW - Quantum control
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U2 - 10.1016/j.cnsns.2023.107219
DO - 10.1016/j.cnsns.2023.107219
M3 - Article
AN - SCOPUS:85151488154
SN - 1007-5704
VL - 122
JO - Communications in Nonlinear Science and Numerical Simulation
JF - Communications in Nonlinear Science and Numerical Simulation
M1 - 107219
ER -