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Published Paper
Title: High fidelity control of a many-body Tonks-Girardeau gas with an effective mean-field approach
Our paper on "High fidelity control of a many-body Tonks-Girardeau gas with an effective mean-field approach" has been published in Physical Review Research 6, 023114 (2024). This work has been done in collaboration with Muhammad S. Hasan, Thomas Fogarty and Thomas Busch (OIST, OKinawa, Japan). The work has been started during the research visit of Muhammad S. Hasan to our research group last year. The paper emanated from research supported in part by a Grant from Science Foundation Ireland under Grant number 19/FFP/6951 (“Shortcut- Enhanced Quantum Thermodynamics”).
Shortcuts to adiabaticity (STA) are powerful tools that can be used to control quantum systems with high fi- delity. They work particularly well for single particle and noninteracting systems which can be described exactly and which possess invariant or self-similar dynamics. However, finding an exact STA for strongly correlated many-body systems can be difficult, as their complex dynamics may not be easily described, especially for larger systems that do not possess self-similar solutions. Here, we design STAs for one-dimensional bosonic gas in the Tonks-Girardeau limit by using a mean-field approach that succinctly captures the strong interaction effects through a quintic nonlinear term in the Schrödinger equation. We show that for the case of the harmonic oscillator with a time-dependent trap frequency the mean-field approach works exactly and recovers the well-known STA from literature. To highlight the robustness of our approach we also show that it works effectively for anharmonic potentials, achieving higher fidelities than other typical control techniques.