Efficient Manipulation of Bose-Einstein Condensates in a Double-Well Potential

Jimmie Adriazola, Roy Goodman, and Panos Kevrekidis. Communications in Nonlinear Science and Numerical Simulation, 2023.
Jul 1, 2023·
Jimmie Adriazola
Jimmie Adriazola
Roy Goodman
Roy Goodman
Panos Kevrekidis
Panos Kevrekidis
· 0 min read
Abstract
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 a 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.
Type
Publication
Communications in Nonlinear Science and Numerical Simulation, 122, 107219
publication published
BEC Nonlinear Schrödinger equation optimal control
Jimmie Adriazola
Authors
Jimmie Adriazola
Presidential Postdoctoral Fellow, Arizona State University

In addition to studying applied mathematics and physics, Jimmie plays jazz guitar in local venues.

Jimmie’s dissertation research focused on the application of methods of optimal control to designing structures for the control of nonlinear waves in optics and BECs. He also worked as a research assistant in the NJIT Physics Department with professors John Federici and Ian Gatley.

Roy Goodman
Authors
Roy Goodman
Professor, Associate Chair for Graduate Studies, Department of Mathematical Sciences

I am a professor in the Department of Mathematical Sciences at NJIT. My research applies methods of dynamical systems to (conservative, dispersive) nonlinear wave equations arising, for example, in optics and fluid mechanics. I am interested in dynamical and bifurcation phenomena, and I use techniques from Hamiltonian mechanics and perturbation theory, as well as extensive computations. My current research in vortex dynamics is supported by the NSF under DMS-2206016.

I led the effort to start the SIAM New York-New Jersey-Pennsylvania Section (SIAM NNP) and was its first president in 2023-2024. I have handed over the reins to a new leadership group.

Panos Kevrekidis
Authors
Panos Kevrekidis
Professor