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Q: Fachverband Quantenoptik und Photonik
Q 43: Ultracold Matter (Bosons) III (joint session Q/A)
Q 43.7: Vortrag
Mittwoch, 12. März 2025, 16:00–16:15, WP-HS
Conformal symmetry as a resource for improved parameter estimation in the nonlinear Schrödinger equation — David B. Reinhardt1, Dean Lee2, •Wolfgang P. Schleich3,4, and Matthias Meister1 — 1German Aerospace Center (DLR), Institute of Quantum Technologies, Ulm, Germany — 2Facility for Rare Isotope Beams and Department of Physics and Astronomy, Michigan State University, USA — 3Institut für Quantenphysik and Center for Integrated Quantum Science and Technology (IQST), Universität Ulm, Germany — 4Hagler Institute for Advanced Study at Texas A&M University, USA
The conformal symmetry of the non-linear Schrödinger equation (NLSE) unifies the stationary and time-dependent travelling-wave solutions of the one-dimensional cubic-quintic NLSE, the cubic NLSE and LSE. Any two systems that are classified by the same single number called the cross-ratio are related by this symmetry [1]. Here, we show that the symmetry serves as a powerful resource in parameter estimation from noisy empirical data, significantly enhancing results through the application of an optimization afterburner that exploits the conformal symmetry with random transformation coefficients. The conformal afterburner optimization finds the true global minimum more reliably compared with a standard fitting approach with randomized initial guesses. The new method demonstrates that group transformations can enhance the performance of search algorithm and therefore has far reaching practical applications for nonlinear physical systems. [1] Reinhardt et al., arXiv:2306.17720 (2023)
Keywords: Conformal symmetry; Bose-Einstein condensates; Solitons; Parameter estimation; Nonlinear optics