High fidelity control of a many-body Tonks–Girardeau gas with an effective mean-field approach
Physical Review Research(2024)
摘要
Shortcuts to adiabaticity (STA) are powerful tools that can be used to
control quantum systems with high fidelity. They work particularly well for
single particle and non-interacting 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.
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