Optimal control of quasi-1D Bose gases in optical box potentials

Andreas Deutschmann-Olek; Katharina Schrom; Nikolaus Würkner; Jörg Schmiedmayer; Sebastian Erne; Andreas Kugi

doi:10.1016/j.ifacol.2023.10.1781

Optimal control of quasi-1D Bose gases in optical box potentials

Andreas Deutschmann-Olek
, Katharina Schrom
, Nikolaus Würkner
, Jörg Schmiedmayer
, Sebastian Erne
, Andreas Kugi

Complex Dynamical Systems

TU Wien, Automation & Control Institute (ACIN)
Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien

Research output: Chapter in Book or Conference Proceedings › Conference Proceedings with Oral Presentation › peer-review

Abstract

In this paper, we investigate the manipulation of quasi-1D Bose gases that are trapped in a highly elongated potential by optimal control methods. The effective mean-field dynamics of the gas can be described by a one-dimensional non-polynomial Schrödinger equation. We extend the indirect optimal control method for the Gross-Pitaevskii equation by Winckel and Borzì (2008) to obtain necessary optimality conditions for state and energy cost functionals. This approach is then applied to optimally compress a quasi-1D Bose gase in an (optical) box potential, i.e., to find a so-called short-cut to adiabaticity, by solving the optimality conditions numerically. The behavior of the proposed method is finally analyzed and compared to simple direct optimization strategies using reduced basis functions. Simulations results demonstrate the feasibility of the proposed approach.

Previous article in issue

Original language	English
Title of host publication	Proceedings of the 22nd IFAC World Congress
Pages	1339-1344
Volume	56
Edition	2
DOIs	https://doi.org/10.1016/j.ifacol.2023.10.1781
Publication status	Published - 22 Nov 2023
Event	22nd IFAC World Congress - Yokohama, Japan Duration: 9 Jul 2023 → 14 Jul 2023

Conference

Conference	22nd IFAC World Congress
Country/Territory	Japan
City	Yokohama
Period	9/07/23 → 14/07/23

Research Field

Complex Dynamical Systems

Keywords

Optimal control
partial differential equations
non-polynomial Schrödinger equation
Bose gases
ultra cold atoms

Access to Document

10.1016/j.ifacol.2023.10.1781

Cite this

@inproceedings{ef941c28421a43a8ba0749db9942de8d,

title = "Optimal control of quasi-1D Bose gases in optical box potentials",

abstract = "In this paper, we investigate the manipulation of quasi-1D Bose gases that are trapped in a highly elongated potential by optimal control methods. The effective mean-field dynamics of the gas can be described by a one-dimensional non-polynomial Schr{\"o}dinger equation. We extend the indirect optimal control method for the Gross-Pitaevskii equation by Winckel and Borz{\`i} (2008) to obtain necessary optimality conditions for state and energy cost functionals. This approach is then applied to optimally compress a quasi-1D Bose gase in an (optical) box potential, i.e., to find a so-called short-cut to adiabaticity, by solving the optimality conditions numerically. The behavior of the proposed method is finally analyzed and compared to simple direct optimization strategies using reduced basis functions. Simulations results demonstrate the feasibility of the proposed approach. Previous article in issue",

keywords = "Optimal control, partial differential equations, non-polynomial Schr{\"o}dinger equation, Bose gases, ultra cold atoms",

author = "Andreas Deutschmann-Olek and Katharina Schrom and Nikolaus W{\"u}rkner and J{\"o}rg Schmiedmayer and Sebastian Erne and Andreas Kugi",

year = "2023",

month = nov,

day = "22",

doi = "10.1016/j.ifacol.2023.10.1781",

language = "English",

volume = "56",

pages = "1339--1344",

booktitle = "Proceedings of the 22nd IFAC World Congress",

edition = "2",

note = "22nd IFAC World Congress ; Conference date: 09-07-2023 Through 14-07-2023",

}

TY - GEN

T1 - Optimal control of quasi-1D Bose gases in optical box potentials

AU - Deutschmann-Olek, Andreas

AU - Schrom, Katharina

AU - Würkner, Nikolaus

AU - Schmiedmayer, Jörg

AU - Erne, Sebastian

AU - Kugi, Andreas

PY - 2023/11/22

Y1 - 2023/11/22

N2 - In this paper, we investigate the manipulation of quasi-1D Bose gases that are trapped in a highly elongated potential by optimal control methods. The effective mean-field dynamics of the gas can be described by a one-dimensional non-polynomial Schrödinger equation. We extend the indirect optimal control method for the Gross-Pitaevskii equation by Winckel and Borzì (2008) to obtain necessary optimality conditions for state and energy cost functionals. This approach is then applied to optimally compress a quasi-1D Bose gase in an (optical) box potential, i.e., to find a so-called short-cut to adiabaticity, by solving the optimality conditions numerically. The behavior of the proposed method is finally analyzed and compared to simple direct optimization strategies using reduced basis functions. Simulations results demonstrate the feasibility of the proposed approach. Previous article in issue

AB - In this paper, we investigate the manipulation of quasi-1D Bose gases that are trapped in a highly elongated potential by optimal control methods. The effective mean-field dynamics of the gas can be described by a one-dimensional non-polynomial Schrödinger equation. We extend the indirect optimal control method for the Gross-Pitaevskii equation by Winckel and Borzì (2008) to obtain necessary optimality conditions for state and energy cost functionals. This approach is then applied to optimally compress a quasi-1D Bose gase in an (optical) box potential, i.e., to find a so-called short-cut to adiabaticity, by solving the optimality conditions numerically. The behavior of the proposed method is finally analyzed and compared to simple direct optimization strategies using reduced basis functions. Simulations results demonstrate the feasibility of the proposed approach. Previous article in issue

KW - Optimal control

KW - partial differential equations

KW - non-polynomial Schrödinger equation

KW - Bose gases

KW - ultra cold atoms

U2 - 10.1016/j.ifacol.2023.10.1781

DO - 10.1016/j.ifacol.2023.10.1781

M3 - Conference Proceedings with Oral Presentation

VL - 56

SP - 1339

EP - 1344

BT - Proceedings of the 22nd IFAC World Congress

T2 - 22nd IFAC World Congress

Y2 - 9 July 2023 through 14 July 2023

ER -

Optimal control of quasi-1D Bose gases in optical box potentials

Abstract

Conference

Research Field

Keywords

Access to Document

Fingerprint

Cite this